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Global dimensions of SU(N) fusion categories
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Numbers
$N$
$k$
$\mathcal G,\mathcal D$ 
$\mathcal G_{N,k}$ or $\mathcal D_{N,k}$
2
1
$\mathcal G$:
2
2
1
$\mathcal D$:
1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
2
2
$\mathcal G$:
4
2
2
$\mathcal D$:
2
2
3
$\mathcal G$:
7.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
2
3
$\mathcal D$:
2.689994047855829307840235875542995023507132444170220604781676580689038116615975306264824043913616550
2
4
$\mathcal G$:
12
2
4
$\mathcal D$:
3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151
2
5
$\mathcal G$:
18.59179388647954474914444835006369868972187449569864544313864520557255890136365813861298587748673263
2
5
$\mathcal D$:
4.311820252106938739469167052845926971456506020069968482228326011710510940603879600463116864062732922
2
6
$\mathcal G$:
27.31370849898476039041350979367758462855737500301558458541343790392585982769685631080310027462113258
2
6
$\mathcal D$:
5.226251859505506111426572693708748614335044753397078110195593467632324165844768203807414880770512573
2
7
$\mathcal G$:
38.46884476685863703107802313456177772646448709613831854733198336899651919823317018973570199822195873
2
7
$\mathcal D$:
6.202325754655154923893473006405067588396003809572966961963623385322168365973183251517027018934055789
2
8
$\mathcal G$:
52.36067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
2
8
$\mathcal D$:
7.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
2
9
$\mathcal G$:
69.29288063023195902562183322502405534688003665711087379249318882761695278373473866784629488013660908
2
9
$\mathcal D$:
8.324234537195114316045836061039976254304452527320080646484602541699966141855608330434716084408459340
2
10
$\mathcal G$:
89.56921938165305504465871219614093680662732609144913507333936750684639240581120088994750848217396582
2
10
$\mathcal D$:
9.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151
2
11
$\mathcal G$:
113.4935300973717472286982810748620164450558833543856930251181029818813388749325794672680280636916685
2
11
$\mathcal D$:
10.65333422442813192849824665965827623201627614550026979468843239375354326599575093743061684638385741
2
12
$\mathcal G$:
141.3696855066245487786220033966543522606988580095825183034702642885920200815279260043290218745254761
2
12
$\mathcal D$:
11.88989846494176537964315627676162188922978226329932948821558717884013058622190039449052997470869997
2
13
$\mathcal G$:
173.5015835025843920058416591912950026240328960944090991767706471023427029133635836208925515808851379
2
13
$\mathcal D$:
13.17199998111844790651870064274396311122406206023417045697637412097814646180375486517442140789403577
2
14
$\mathcal G$:
210.1931389527054428452703448457747777855445220945120823345847541587162731176161218314214759750706851
2
14
$\mathcal D$:
14.49803914164620548963976491001715834969995634304468846759232543018355546955397926317471923889025131
2
15
$\mathcal G$:
251.7482785237480696996058551601439926331175885886831336099289496676837614885955480475120059637855151
2
15
$\mathcal D$:
15.86657740420876242918942852712480680478054192311527422007222295315890831722190602102273784285139105
2
16
$\mathcal G$:
298.4709372977372258383640067747513321941939082438713648664925399337230423811030621827959160576640132
2
16
$\mathcal D$:
17.27631144943090060864931132789677763923449761117357559708343995329065453195067350739695067805537681
2
17
$\mathcal G$:
350.6650564931198741553560893431965166649029637684607658953083960437414798790213674975763150843911606
2
17
$\mathcal D$:
18.72605288076266952618939802270329153819163462079553840316703903578003591593362242425224978840168789
2
18
$\mathcal G$:
408.6345818906140097284937164610780138503487108560327438481865913858276221721313128522637500795004189
2
18
$\mathcal D$:
20.21471201601976841104292597682393942872586911648274599118009416001040325055300436518644686792152304
2
19
$\mathcal G$:
472.6834627213292167453887742349214931718283788106067376079711714392403439350810388041847715225361964
2
19
$\mathcal D$:
21.74128475323685228019727678584181146755145604595024009846440928225705615576057521745603454588509679
2
20
$\mathcal G$:
543.1156508657905174239691597627230679076175907068441153717992175409455577135275470771836807944273115
2
20
$\mathcal D$:
23.30484179019009168574864255522869840586214224951171538575654169818262697446699991468444268005108853
3
1
$\mathcal G$:
3
3
1
$\mathcal D$:
1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576
3
2
$\mathcal G$:
10.85410196624968454461376050309691435316092753941728858640634586811578138845670734912162161256817341
3
2
$\mathcal D$:
3.294556414185327703509680157112760012118642055644945569405262031857126869661478038291826897629751409
3
3
$\mathcal G$:
36
3
3
$\mathcal D$:
6
3
4
$\mathcal G$:
106.0272641299684115839665025474907641955241435071868887276026982164440150611459445032467664058941071
3
4
$\mathcal D$:
10.29695411905716959643390026960721029765619777646081156612056957574964165213142489044765538890644006
3
5
$\mathcal G$:
279.7645019878171246849621175241310155426885000361870150249612548471103179323622757296372032954535910
3
5
$\mathcal D$:
16.72616220140822156689892166484705503563501093786820302595399818681157357746446025448402247944755524
3
6
$\mathcal G$:
671.5596089199087581363190152431904974369362935487105709496082148508768453574818899112908111297440298
3
6
$\mathcal D$:
25.91446717414635091297396699184516645885174641676036339562515992993598179792601026109542601708306521
3
7
$\mathcal G$:
1487.902432574930599815027310681321157695404058671803489009396090985471905460475616806756754764998151
3
7
$\mathcal D$:
38.57333836440567403090098197835586366120673239138437646389339943218820935084156012845418797734086433
3
8
$\mathcal G$:
3080.071811302179586660265839804194055252385437330550985682661671205568689378732147080206938422302754
3
8
$\mathcal D$:
55.49839467319914819033477541360811929621235231957233526930232256985071126928457565876689075715354518
3
9
$\mathcal G$:
6016.983795479019963215427278122147450077167478584337725280434460492940253218406464076220610716525539
3
9
$\mathcal D$:
77.56921938165305504465871219614093680662732609144913507333936750684639240581120088994750848217396582
3
10
$\mathcal G$:
11182.90988911172424093379738748833683066576124028413195764358730772191810339231168172847518709513827
3
10
$\mathcal D$:
105.7492784330546826683650700976415489185191149951177542894264903619060748972444700281523702247734405
3
11
$\mathcal G$:
19905.22575374912729586004549437813578202488610801893861659443183527668432099044229049374677222404546
3
11
$\mathcal D$:
141.0858807739070936685083435136839660541520986410907772248812279678881668368525511858767067592666596
3
12
$\mathcal G$:
34117.84233043195023081051398751841184749018269546566936680419194293030023250879638619400263710092969
3
12
$\mathcal D$:
184.7101576265689570017036369833080450254053542760516189935277127101860683861710358760398953805705742
3
13
$\mathcal G$:
56566.46282445714596887958141233340997736452367416034410952962689756417813797334583757654174153960425
3
13
$\mathcal D$:
237.8370509917602093224988886654257577260948817076549187098139962355526036077885487696458918905610111
4
1
$\mathcal G$:
4
4
1
$\mathcal D$:
2
4
2
$\mathcal G$:
24
4
2
$\mathcal D$:
4.898979485566356196394568149411782783931894961313340256865385134501920754914630053079718866209280470
4
3
$\mathcal G$:
141.3696855066245487786220033966543522606988580095825183034702642885920200815279260043290218745254761
4
3
$\mathcal D$:
11.88989846494176537964315627676162188922978226329932948821558717884013058622190039449052997470869997
4
4
$\mathcal G$:
746.0386719675123324932323133976827081138360000964987067332300129256275144862994019456992087878762426
4
4
$\mathcal D$:
27.31370849898476039041350979367758462855737500301558458541343790392585982769685631080310027462113258
4
5
$\mathcal G$:
3473.651247572846710060368081297015986330326898926456378397910479204676508573236746193550992691968159
4
5
$\mathcal D$:
58.93768953371727406215604626912355545292897419227663709466396673799303839646634037947140399644391746
4
6
$\mathcal G$:
14355.41752799932702850935573994008395340997875075688231766687118531366696204097567812612610681210328
4
6
$\mathcal D$:
119.8140956982913885920454198570422938171779778015822594642172865754811879112690459809004635406916688
4
7
$\mathcal G$:
53267.79648807196880999888648818957314715784022597727177294297808710869887248081978822401031141210349
4
7
$\mathcal D$:
230.7981726272371698346302744244281762925039063071410574713590443379375962284604403591547003297340266
4
8
$\mathcal G$:
179645.5138643705988964628183436644235023150243575301317584130338147882075965521939222866183214957662
4
8
$\mathcal D$:
423.8460969082652752232935609807046840331366304572456753666968375342319620290560044497375424108698291
4
9
$\mathcal G$:
556850.0941033340777391691990128395637944464194881392679754905767583077165907980677861590711517940161
4
9
$\mathcal D$:
746.2238900647272078993474649882853622678688015939287575821916632945015945225336817529752632994334347
4
10
$\mathcal G$:
1602163.009810273426091955124157730964127626801858715696067770079441287238315055305633077823990570893
4
10
$\mathcal D$:
1265.765779996549529918538016730847274075528144048945118668950761834078860921092638745968138463032498
4
11
$\mathcal G$:
4315288.028879059210060322567817900895937901678556558722314942218854295693565297291232347341339498623
4
11
$\mathcal D$:
2077.327135739351769097668271047267939572845496938752326170904740590099503626197297920496651227686318
4
12
$\mathcal G$:
10959962.25354690704090154885312176838024302658606448474793957882828251668877928475514112623127449420
4
12
$\mathcal D$:
3310.583370577896659428876473837708176542623457534478255340190051131193140850324280395506182321912316
5
1
$\mathcal G$:
5
5
1
$\mathcal D$:
2.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
5
2
$\mathcal G$:
46.47948471619886187286112087515924672430468623924661360784661301393139725340914534653246469371683159
5
2
$\mathcal D$:
6.817586428949680860280487165008196984463525773655422919873880935759509433382391259589900386297653491
5
3
$\mathcal G$:
466.2741699796952078082701958735516925711475000603116917082687580785171965539371262160620054924226516
5
3
$\mathcal D$:
21.59338255067267611363226885265597907664069399574697020451360839281246145710817248303465006703233028
5
4
$\mathcal G$:
4342.064059466058387575460101621269982912908623658070472997388099005845635716545932741938740864960199
5
4
$\mathcal D$:
65.89434011708485413061726572292360005242187863282963341400260849098339399408788503173517219924007069
5
5
$\mathcal G$:
35888.54381999831757127338934985020988352494687689220579416717796328416740510243919531531526703025820
5
5
$\mathcal D$:
189.4427190999915878563669467492510494176247343844610289708358898164208370255121959765765763351512910
5
6
$\mathcal G$:
260944.6823457600577714988228813876545858234810206930136048982463069004273955442648382810938126759308
5
6
$\mathcal D$:
510.8274487004002585242231352656181583372922750767395140159256886028627357653234611859558339185458034
5
7
$\mathcal G$:
1676115.462734125589700319637874201286021606894003614563078521648938023270901153809941341771000627151
5
7
$\mathcal D$:
1294.648779682785469275958603758050690426828934057106667456730799385295186029100288662591628925346446
5
8
$\mathcal G$:
9595120.032520102214704921763851608757130024683366034678512402150418400117406822956660147595180430763
5
8
$\mathcal D$:
3097.599075497037627353029113499280103306171640511081678951143642708524191126262969052842623118853570
5
9
$\mathcal G$:
49446012.01704735545802919889019310180851286756637768268894167965790672538560336069917135929914408976
5
9
$\mathcal D$:
7031.785834128294571578723894415505992759375963826620040767246668485197253282397281443750576304588977
5
10
$\mathcal G$:
231634043.2211672141052593826687974268733711160273257377512102857302929614013257054225194463315143493
5
10
$\mathcal D$:
15219.52835081190070533953832785713714422472126667073231766342619156379470847905787736196011326550705
5
11
$\mathcal G$:
995406276.8711347770361601298069324998182507165336692823720868348490367704922113632967136074933508148
5
11
$\mathcal D$:
31550.05985527023967766553545138349987637416364383596595899495746359936407552938043055636004771644511
6
1
$\mathcal G$:
6
6
1
$\mathcal D$:
2.449489742783178098197284074705891391965947480656670128432692567250960377457315026539859433104640235
6
2
$\mathcal G$:
81.94112549695428117124052938103275388567212500904675375624031371177757948309056893240930082386339775
6
2
$\mathcal D$:
9.052133753814858494368103213730148568916268810603021935270449624162269839566121883103505113720126391
6
3
$\mathcal G$:
1343.119217839817516272638030486380994873872587097421141899216429701753690714963779822581622259488060
6
3
$\mathcal D$:
36.64859093935014462894675915312413167408220155306566013627296186651560055275603256594039315363678139
6
4
$\mathcal G$:
21533.12629199899054276403360991012593011496812613532347650030677797050044306146351718918916021815492
6
4
$\mathcal D$:
146.7416992269034294446831616558828868943706442582470416539837545003469825150915821536315950074634134
6
5
$\mathcal G$:
313133.6188149120693257985874576651855029881772248316163258778955682805128746531178059373125752111170
6
5
$\mathcal D$:
559.5834332920445468589387010208559398168255511622875235442024132931103793975037106961692776684425708
6
6
$\mathcal G$:
4022677.110561901415280767130898083086451856545608674951388451957451255850162769143859220250401505162
6
6
$\mathcal D$:
2005.661265159673321071809092707382483359055826194779241760144820164313417739468821358740203572175180
6
7
$\mathcal G$:
45387415.95675909525299040449022695608237717548693377698263155999674414740569278216111589150678465670
6
7
$\mathcal D$:
6737.018328367460753986490942236504159283341084514809285396057666574834148070498145882009719528687291
6
8
$\mathcal G$:
451177581.5344124301632626656377854068264568117918898021155095950667110072290993135039273343123175871
6
8
$\mathcal D$:
21240.94116404478980598292710169161830493319238019017236598061456432420332098997687398692551389479435
6
9
$\mathcal G$:
3978734554.535703930477371085255471101402833613267488788937557721110155226039041390454813220855034267
6
9
$\mathcal D$:
63077.21105546522124607713170275699931445789758891656895070531751062318552394719176414507277236496980
6
10
$\mathcal G$:
31384135480.31544273354556182973885830363182173241678761925690542498994599671162534665947363265519149
6
10
$\mathcal D$:
177155.6814790749033445695676424008801468617709758933855809095472147520393819036123204845619447299044
7
1
$\mathcal G$:
7
7
1
$\mathcal D$:
2.645751311064590590501615753639260425710259183082450180368334459201068823230283627760392886474543611
7
2
$\mathcal G$:
134.6409566840052296087730809709662220426257048364841149156619417914878171938160956640749569937768556
7
2
$\mathcal D$:
11.60348898754186044617993087374453110598710335497022669488621709025279963772845223892586120206870558
7
3
$\mathcal G$:
3471.772342674838066235063724923082701289276136900874807688590878966101112741109772549099094451662352
7
3
$\mathcal D$:
58.92174762067769885535011265492857973357428176063063179496822333701705929464457686774268522741047412
7
4
$\mathcal G$:
93218.64385412594541749805135433175300752622039546022560265021165244022302684143462939201804497118110
7
4
$\mathcal D$:
305.3172839099122233272948999646226445255957638987646791500198108375439049995310104037972878592591541
7
5
$\mathcal G$:
2346561.647827775825580447493023881800430249651605060388309930308513232579261615333917878479400878011
7
5
$\mathcal D$:
1531.849094339183211171257265594412428753943349624764931584097001066261716582347193744525893299567325
7
6
$\mathcal G$:
52951985.28288561112848880523859811542944003806808940647973681999620150530664157918796854009124876615
7
6
$\mathcal D$:
7276.811477761782109784654330121390080843552828427754713510697193926313940846138538615543186066398342
7
7
$\mathcal G$:
1052747690.246962337047612886488165949261732560847742871602855721822325683534565064842497113395407703
7
7
$\mathcal D$:
32446.07357211288727813774407708787095253935775023760110240370224165234555236579954939985660286987837
7
8
$\mathcal G$:
18364556497.02680928208905924715844155442115840066620560691073174379490296176821806483861584375505627
7
8
$\mathcal D$:
135515.8902012114935067872635745024012430112000406423132346776225506749250203342352214066491618394434
7
9
$\mathcal G$:
281770047515.3207560102869169570583668359325948107129218171637447495969508064624026332318948341895914
7
9
$\mathcal D$:
530820.1649479047023463897579318978189564133189804149165672273734664241028361739611837249946407792336
8
1
$\mathcal G$:
8
8
1
$\mathcal D$:
2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145
8
2
$\mathcal G$:
209.4427190999915878563669467492510494176247343844610289708358898164208370255121959765765763351512910
8
2
$\mathcal D$:
14.47213595499957939281834733746255247088123671922305144854179449082104185127560979882882881675756455
8
3
$\mathcal G$:
8213.524830139145564427375572811184147339694499548135961820431123214849838343285725547218502459474011
8
3
$\mathcal D$:
90.62849899528925533901419054479859496782015347791700042664466665540876975746187458890262732403398600
8
4
$\mathcal G$:
359291.0277287411977929256366873288470046300487150602635168260676295764151931043878445732366429915323
8
4
$\mathcal D$:
599.4088986065699023248388533940017520069628227602211992180859314761134606426929235764668393873274079
8
5
$\mathcal G$:
15352192.05203216354352787482216257401140803949338565548561984344066944018785091673065623615228868922
8
5
$\mathcal D$:
3918.187342641002859316188122751462498724110745722183986388374139418955895787390882009304980955682553
8
6
$\mathcal G$:
601570108.7125499068843502208503805424352757490558530694873461267556146763054657513385697790830901161
8
6
$\mathcal D$:
24526.92619780452445931708531827040776670011277867675663885143070526328612226512387458476563508917687
8
7
$\mathcal G$:
20988064568.03063917953035342532393320505275245790423497932655056433703195630653493124413239286292145
8
7
$\mathcal D$:
144872.5804561741047596292534172951449072317485730350606756012867990495762127100600892965545819080061
8
8
$\mathcal G$:
644045822892.1617280235129530447048384821316452816295355820885594276501732719140631616729024781476376
8
8
$\mathcal D$:
802524.6556288234861943861252805021426952356430593945029874745526061076747022482765528092648668627289
9
1
$\mathcal G$:
9
9
1
$\mathcal D$:
3
9
2
$\mathcal G$:
311.8179628360438156152982495126082490609601649569989320662193497242762875268063240053083269606147409
9
2
$\mathcal D$:
17.65836806831378219517583424761239051220079224781210509263136777941508142879281586469223974280239190
9
3
$\mathcal G$:
18050.95138643705988964628183436644235023150243575301317584130338147882075965521939222866183214957662
9
3
$\mathcal D$:
134.3538290724795825669880682942114052099409891371737026100090512602695886087168013349212627232609487
9
4
$\mathcal G$:
1252912.711732501674913130697778889018537504443848313352944853797706192362329295652518857910091536536
9
4
$\mathcal D$:
1119.335835097090811849021197482428043401803202390893136373287494941752391783800522629462894949150152
9
5
$\mathcal G$:
89002821.63068523982445255800234758325532316161947982884009502338423210569408604925850844673845936158
9
5
$\mathcal D$:
9434.130676998556385030056326742748690137235402585423976536098971888430393444292435329507149873013133
9
6
$\mathcal G$:
5968101831.803555895716056627883206652104250419901233183406336581665232839058562085682219831282551400
9
6
$\mathcal D$:
77253.49074186587133701717277272191001686801492908419864816735437662230688615368778716837170124827715
9
7
$\mathcal G$:
362275775376.8409720132260360876464716461990504709166137649248146780532224654516605284410076439580461
9
7
$\mathcal D$:
601893.4917216176146457895939603766070214267322945458772406059144545807560266862074146069486501470467
10
1
$\mathcal G$:
10
10
1
$\mathcal D$:
3.162277660168379331998893544432718533719555139325216826857504852792594438639238221344248108379300295
10
2
$\mathcal G$:
447.8460969082652752232935609807046840331366304572456753666968375342319620290560044497375424108698291
10
2
$\mathcal D$:
21.16237455741357194881357281195245663430955356825233599880053100469009173770078746352506120399004069
10
3
$\mathcal G$:
37276.36629703908080311265795829445610221920413428043985881195769240639367797437227242825062365046089
10
3
$\mathcal D$:
193.0708841255953869961522958676182237849503401510898105367145718707271129632754909385089262788208604
10
4
$\mathcal G$:
4005407.524525683565229887810394327410319067004646789240169425198603218095787638264082694559976427233
10
4
$\mathcal D$:
2001.351424544346126023885924363555231750252537178478911282130484557089654157849400297252570027872284
10
5
$\mathcal G$:
463268086.4423344282105187653375948537467422320546514755024205714605859228026514108450388926630286986
10
5
$\mathcal D$:
21523.66340664001436127339211733997754896650615516774612571293697358236290689231951102016071711622846
10
6
$\mathcal G$:
52306892467.19240455590926971623143050605303622069464603209484237498324332785270891109912272109198581
10
6
$\mathcal D$:
228707.0013514942759280924760716385341985803985063060104134071068652760957167340296386815368220551458
11
1
$\mathcal G$:
11
11
1
$\mathcal D$:
3.316624790355399849114932736670686683927088545589353597058682146116484642609043846708843399128290651
11
2
$\mathcal G$:
624.2144155355446097578405459117410904478073584491213116381495664003473638121291870699741543503041769
11
2
$\mathcal D$:
24.98428337046201150770943828112859620715086035676576038196953822929191739556525961881835295080370796
11
3
$\mathcal G$:
72985.82776374680008482016681271983120075791572940277492751291672934784251029828839847707149815483337
11
3
$\mathcal D$:
270.1588935492348363730548402250513868547044253927851911004533258972801933257593556300278548342378106
11
4
$\mathcal G$:
11867042.07941741282766588706149922746382922961603053648636609110184931315730456755088895518868362121
11
4
$\mathcal D$:
3444.857338035555403261901766858902504865714766378853983347853663793542407702700828702032033392692742
11
5
$\mathcal G$:
2189893809.116496509479552285575251499600151576374072421218591036667880895082864999252769936485371793
11
5
$\mathcal D$:
46796.30123328655244628134960179515854697978669871654810658055379804244731573064495075153664177325628
12
1
$\mathcal G$:
12
12
1
$\mathcal D$:
3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151
12
2
$\mathcal G$:
848.2181130397472926717320203799261135641931480574951098208215857315521204891675560259741312471528564
12
2
$\mathcal D$:
29.12418433260830899233854602822471547310162406725166094301809855050192425845905661920359330452739040
12
3
$\mathcal G$:
136471.3693217278009232420559500736473899607307818626774672167677717212009300351855447760105484037188
12
3
$\mathcal D$:
369.4203152531379140034072739666160900508107085521032379870554254203721367723420717520797907611411484
12
4
$\mathcal G$:
32879886.76064072112270464655936530514072907975819345424381873648484755006633785426542337869382348260
12
4
$\mathcal D$:
5734.098600533541673177714439925050302806944989548839627492372985508071721967782120110440784127110851
13
1
$\mathcal G$:
13
13
1
$\mathcal D$:
3.605551275463989293119221267470495946251296573845246212710453056227166948293010445204619082018490718
13
2
$\mathcal G$:
1127.760292766798548037970784743417517056213824613659144649009206165227568936863293535801585275753396
13
2
$\mathcal D$:
33.58214246838337960477596239620091150057089493171590718159747108581121375972150532565025637331322247
13
3
$\mathcal G$:
245121.3389059809658651448527867781099019129359213614911412950498894447719312178319628316808800049518
13
3
$\mathcal D$:
495.0973024628400920380332652156151377669545311490107365155374977252669014921871549777240895542222202
14
1
$\mathcal G$:
14
14
1
$\mathcal D$:
3.741657386773941385583748732316549301756019807778726946303745467320035156306939027976809895194379572
14
2
$\mathcal G$:
1471.351972668938099916892413920423444498811654661584576342093279111013911823312852819950331825494795
14
2
$\mathcal D$:
38.35820606687619978166427174257512273914369945125250121801066810889257076109395921691046101006662969
15
1
$\mathcal G$:
15
15
1
$\mathcal D$:
3.872983346207416885179265399782399610832921705291590826587573766113483091936979033519287376858673518
15
2
$\mathcal G$:
1888.112088928110522747043913701079944748381914415123502074467122507628211164466610356340044728391363
15
2
$\mathcal D$:
43.45241177343451580334741008666498742278806568193030842432526089981032032150263693885699721120009251
16
2
$\mathcal G$:
2387.767498381897806706912054198010657553551265950970918931940319469784339048824497462367328461312106
16
2
$\mathcal D$:
48.86478791913352617192901220416550889877626873742088018169728248868746740367471008792052420484904185
17
2
$\mathcal G$:
2980.652980191518930320526759417170391651675192031916510110121366371802578971681623729398678217324865
17
2
$\mathcal D$:
54.59535676402819267797656226146681565728421431019725514563463879647771049042652021279628038117768035
18
2
$\mathcal G$:
3677.711237015526087556443448149702124653138397704294694633679322472448599549181815670373750715503770
18
2
$\mathcal D$:
60.64413604805930523312877793047181828617760734944823797354028248003120975165901309555934060376456912
19
2
$\mathcal G$:
4490.492895852627559081193355231754185132369598700764007275726128672783267383269868639755329464093866
19
2
$\mathcal D$:
67.01114008769457997126189764041997955225988403258792572568116181861210110691298571545758914649757103
20
2
$\mathcal G$:
5431.156508657905174239691597627230679076175907068441153717992175409455577135275470771836807944273115
20
2
$\mathcal D$:
73.69638056687658778416677874684676991302266906681950431401793452129719359009320206120919171427963483
Definition
The global dimension $\mathcal G_{N,k}$ of the unitary $SU(N)$ fusion category at level $k$ is the sum of squared quantum dimensions of all simple objects [1]. The two invertible normalisations are $\mathcal G$ and the total quantum dimension $\mathcal D=\sqrt{\mathcal G}>0$ [3].
Parameters
$N$
—   matrix size ($N\geq2$)
$k$
—   level ($k\geq1$)
$\mathcal G,\mathcal D$
—   normalisation (global or total)
Formulas
(1)
$\displaystyle \mathcal G_{N,k}=\sum_{\lambda\in P^+_{N,k}}d_{N,k}(\lambda)^2$, where $d_{N,k}(\lambda)$ is the quantum dimension and $P^+_{N,k}$ is the full integrable alcove [1].
(2)
$\displaystyle \mathcal G_{N,k}=\frac{N m^{N-1}}{\prod_{j=1}^{N-1}(2\sin(\pi j/m))^{2(N-j)}},\qquad m=N+k$ [1] [4].
(3)
$\displaystyle S_{0,0}=\frac{\prod_{j=1}^{N-1}(2\sin(\pi j/m))^{N-j}}{\sqrt{N m^{N-1}}},\quad \mathcal G_{N,k}=S_{0,0}^{-2},\quad \mathcal D_{N,k}=S_{0,0}^{-1}>0$, where $0$ denotes the vacuum and $S$ is the unitary modular matrix [2].
(4)
$\displaystyle k\mathcal G_{N,k}=N\mathcal G_{k,N}$ for $N,k\geq2$ [1].
(5)
$\displaystyle \mathcal G_{N,1}=N,\qquad\mathcal D_{N,1}=\sqrt N$; the $N$ simple objects at level $1$ all have quantum dimension $1$.
(6)
$\displaystyle \mathcal D_{2,k}=\sqrt{\frac{k+2}{2}}\,\csc\!\left(\frac{\pi}{k+2}\right)$ [3].
Comments
(7)
$N$ is the matrix size, so the Lie rank is $N-1$. Set $m=N+k$ and $q=\exp(\pi i/m)$, with $[a]_q=(q^a-q^{-a})/(q-q^{-1})=\sin(\pi a/m)/\sin(\pi/m)$. Long roots have squared length $2$, and dimensions use the positive unitary embedding [1]. A convention that calls $\exp(2\pi i/m)$ its deformation parameter uses $q^2$ in this notation.
(8)
This is the standard semisimple category of integrable $SU(N)$ Wess–Zumino–Witten representations. No quotient to $PSU(N)$, conformal extension, doubling or Galois conjugation is taken.
(9)
The simple objects are indexed by $\lambda=\sum_{i=1}^{N-1}a_i\omega_i$, where the fundamental weights $\omega_i$ follow the $A_{N-1}$ chain, $a_i\geq0$, and $\sum_i a_i\leq k$. Write $P^+_{N,k}$ for this entire integrable alcove, including the vacuum and every dimension-one object.
(10)
The global and total dimensions are two invertible conventions for the same positive quantity. Both use the same category indices, with $\mathcal G=\mathcal D^2$ and $\mathcal D>0$.
(11)
The individual quantum dimensions $d_{N,k}(\lambda)$ are tabulated for 37 complete alcoves. The sum defining $\mathcal G$ uses every weight in $P^+_{N,k}$, including dimension-one rows, even when a companion table does not list the whole alcove.
(12)
The Witten zeta values sum inverse powers of ordinary dimensions over infinitely many representations. Here the sum is finite and uses squared quantum dimensions; neither is a stored specialization of the other.
Programs
(P1)
Sage
def global_dimension(N, k, prec=429):
    assert N in ZZ and N >= 2 and k in ZZ and k >= 1
    m = N+k
    K = CyclotomicField(m)
    z = K.gen()
    R = RealBallField(prec)
    exact_den, ball_den = K.one(), R.one()
    for j in range(1, N):
        exact_den *= (2-z**j-z**(-j))**(N-j)
        ball_den *= (2*(R.pi()*j/m).sin())**(2*(N-j))
    exact = K(N)*K(m)**(N-1)/exact_den
    return QQ(exact) if exact in QQ else R(N)*R(m)**(N-1)/ball_den

global_dimension(3, 3)  # 36; its positive square root is the total dimension
References
[1]
R. Coquereaux, Quantum McKay correspondence and global dimensions for fusion and module-categories associated with Lie groups, Journal of Algebra 398 (2014), 258–283, Sections 2.1–2.3. (arXiv)
[2]
R. Coquereaux, Global dimensions for Lie groups at level k and their conformally exceptional quantum subgroups, preprint (2010), Section 2.2. (arXiv)
[3]
A. Kitaev and J. Preskill, Topological entanglement entropy, Physical Review Letters 96 (2006), 110404, equations (3)–(4). (arXiv) (doi)
Links
Similar tables
Quantum dimensions of SU(N) WZW representations —   give the individual positive dimensions whose squares sum to $\mathcal G_{N,k}$
Witten zeta values of simple Lie algebras —   are infinite sums of inverse powers of ordinary representation dimensions, in contrast to the finite quantum-dimension sum
Data properties
Entries are of type: real number
How well the digits are known: proven
Table is complete: no (it holds both normalisations for every $N\geq2$, $k\geq1$ with $N+k\leq16$, together with $(N,k)=(2,j),(j,2)$ for $15\leq j\leq20$; the shifted-level bound gives breadth across type-$A$ ranks while bounding cyclotomic order and the cost of full-alcove checks, and the rank-one extension retains all categories of the companion representation table and their level–rank partners; these are noncanonical computational cutoffs on discrete category indices, explained in the attached argument-selection.md)
How they were obtained:

Exact arithmetic in $\mathbb Q(\zeta_{N+k})$ determines every rational global dimension, where $\zeta_m=\exp(2\pi i/m)$. A rational total dimension occurs exactly when the global dimension is a rational square; these 22 rational rows are written exactly. All other values are enclosed by Arb arithmetic throughout the sine product and positive square root, using 429 working bits. The smallest measured accuracy is 418 bits, and the values are written to 100 significant digits.

more

The attached checks.py independently sums squared quantum Weyl dimensions over all 117 complete alcoves, comprising 66,595 simple objects, at 600 bits. These sums agree with separate evaluations of the exact cyclotomic global dimensions and lie inside every written decimal interval. Known-answer and deliberate-error controls precede the comparisons. The checks also cover the positive square-root convention, all level–rank pairs, all level-one values, and the $SU(2)$ formula of [3]. The live mode repeats the checks on the database entries and compares the dimension-square sums from all 37 alcoves of the companion representation table. The attached numerical-evidence.json records precision, sizes, controls and results.



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