QuantumGroupsPath = "~/projects/QuantumGroups/trunk/package/";
AppendTo[$Path, QuantumGroupsPath];
<<QuantumGroups`

RootFromLevel[G2,3]

LevelFromRoot[E6,42]

AlcoveDimensions[Γ_,level_]:=AlcoveDimensions[Γ,level]=
ToRadicals[RootReduce[ExpToTrig[(qDimension[Γ][Irrep[Γ][#]]/.q->Exp[2π I/RootFromLevel[Γ,level]])]]&/@AlcoveWeights[Γ,RootFromLevel[Γ,level]]]

LCM@@NumberFieldDiscriminant[AlcoveDimensions[G2,3]]

Clear[d]

Factors[x_]:=DeleteCases[First/@FactorInteger[x],1]

d[Γ_,l_]:=d[Γ,l]=Union@@(Factors/@NumberFieldDiscriminant[AlcoveDimensions[Γ,l]])

d[A1,#]&/@Range[14]

d[A2,#]&/@Range[10]

d[B2,#]&/@Range[10]

d[G2,#]&/@Range[6]

d[B3,#]&/@Range[6]

d[C3,#]&/@Range[6]

d[A4,#]&/@Range[7]

d[B4,#]&/@Range[6]

d[C4,#]&/@Range[5]

d[D4,#]&/@Range[5]

d[F4,#]&/@Range[8]

d[E6,#]&/@Range[5]

d[E7,#]&/@Range[4]

d[E8,#]&/@Range[3]

N[%]

Sort[N[AlcoveDimensions[E6,5]]]

%/3

ToRadicals[ReducedDimensionsByDepth[HaagerupAsaedaBigraph]]

N[%]

DisplayBigraph[DHAP=GraphFromString["gbg1v1v1v1p1v1x0p1x0v1x1p1x0v0x1"]]

ToRadicals[ReducedDimensionsByDepth[DHAP]]

N[%]

N[AlcoveDimensions[F4,8]]

N[AlcoveDimensions[B4,6]]