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

AlcoveWeights[A3,RootFromLevel[A3,3]]

TwistFactor[Γ_,V:Irrep[Γ_][λ_]]:=(q^(KillingForm[Γ][λ,λ+2ρ[Γ]]))

TwistFactor[A3,Irrep[A3][{0,0,3}]]

SteinbergDecomposeRepresentation[A3,RootFromLevel[A3,3]][Irrep[A3][{0,0,3}]⊗Irrep[A3][{0,0,3}]]

SteinbergDecomposeRepresentation[A3,RootFromLevel[A3,3]][Irrep[A3][{0,0,3}]⊗Irrep[A3][{0,3,0}]]

SteinbergDecomposeRepresentation[A3,RootFromLevel[A3,3]][Irrep[A3][{0,0,3}]⊗Irrep[A3][{3,0,0}]]

RootFromLevel[G2,1/3]

SteinbergDecomposeRepresentation[G2,RootFromLevel[G2,1/3]][((Irrep[G2][{0,2}])^(⊗2))]

TwistFactor[G2,Irrep[(Subscript[G, 2])][{0,0}]]

TwistFactor[G2,Irrep[(Subscript[G, 2])][{0,1}]]

TwistFactor[G2,Irrep[(Subscript[G, 2])][{0,2}]]

TwistFactor[G2,Irrep[(Subscript[G, 2])][{1,2}]]

Mod[78,26]

Mod[8 23,26]

Table[Mod[(k^4),26],{k,1,15}]

Mod[17 23,26]

BraidingMap[G2,Irrep[(Subscript[G, 2])][{0,2}]⊗Irrep[(Subscript[G, 2])][{0,2}],FundamentalBasis]

BraidingMap[G2,Irrep[(Subscript[G, 2])][{0,2}]⊗Irrep[(Subscript[G, 2])][{0,2}],FundamentalBasis][[-1,All,1]]

BraidingMap[G2,Irrep[(Subscript[G, 2])][{0,2}]⊗Irrep[(Subscript[G, 2])][{0,2}],FundamentalBasis][{0,2}]

Eigenvalues[(%86//MatrixData)/.q->1.1]

Log[Abs[%]]/Log[1.1]

Sign[Chop[%96]]

Transpose[{%97,%99}]

Eigenvalues[(BraidingMap[G2,Irrep[(Subscript[G, 2])][{0,2}]⊗Irrep[(Subscript[G, 2])][{0,2}],FundamentalBasis][{0,1}]//MatrixData)/.q->1.1]

Log[Abs[%102]]/Log[1.1]

Sign[Chop[%102]]

Transpose[{%%,%}]

Eigenvalues[(BraidingMap[G2,Irrep[(Subscript[G, 2])][{0,2}]⊗Irrep[(Subscript[G, 2])][{0,2}],FundamentalBasis][{0,0}]//MatrixData)/.q->1.1]

Log[Abs[%103]]/Log[1.1]

Sign[Chop[%103]]

Transpose[{%%,%}]

DecomposeRepresentation[G2][Irrep[(Subscript[G, 2])][{0,2}]⊗Irrep[(Subscript[G, 2])][{0,2}]]

Log[-%%]/Log[13.]

Eigenvalues[BraidingMap[G2,Irrep[(Subscript[G, 2])][{0,2}]⊗Irrep[(Subscript[G, 2])][{0,2}],FundamentalBasis][{0,2}]//MatrixData]

Eigenvalues[BraidingMap[G2,Irrep[(Subscript[G, 2])][{0,2}]⊗Irrep[(Subscript[G, 2])][{0,2}],FundamentalBasis][{0,1}]//MatrixData]

Eigenvalues[BraidingMap[G2,Irrep[(Subscript[G, 2])][{0,2}]⊗Irrep[(Subscript[G, 2])][{0,2}],FundamentalBasis][{0,0}]//MatrixData]

Eigenvalues[BraidingMap[G2,Irrep[(Subscript[G, 2])][{0,2}]⊗Irrep[(Subscript[G, 2])][{0,2}],FundamentalBasis][{-9,2}]//MatrixData]

Eigenvalues[BraidingMap[G2,Irrep[(Subscript[G, 2])][{0,2}]⊗Irrep[(Subscript[G, 2])][{0,2}],FundamentalBasis][{-12,4}]//MatrixData]

Eigenvalues[BraidingMap[G2,Irrep[(Subscript[G, 2])][{0,2}]⊗Irrep[(Subscript[G, 2])][{0,2}],FundamentalBasis][{2,2}]//MatrixData]

RootFromLevel[G2,2/3]

AlcoveWeights[G2,RootFromLevel[G2,2/3]]

SteinbergDecomposeRepresentation[G2,RootFromLevel[G2,2/3]][((Irrep[G2][#])^(⊗2))]&/@AlcoveWeights[G2,RootFromLevel[G2,2/3]]//TableForm

AlcoveWeights[C3,RootFromLevel[C3,3]]

Irrep[C3][#]->SteinbergDecomposeRepresentation[C3,RootFromLevel[C3,3]][Irrep[C3][#]⊗Irrep[C3][{1,0,0}]]&/@AlcoveWeights[C3,RootFromLevel[C3,3]]//TableForm

Irrep[C3][#]->SteinbergDecomposeRepresentation[C3,RootFromLevel[C3,3]][Irrep[C3][#]⊗Irrep[C3][{0,1,0}]]&/@AlcoveWeights[C3,RootFromLevel[C3,3]]//TableForm

Length[AlcoveWeights[C3,RootFromLevel[C3,3]]]

Irrep[C3][#]->SteinbergDecomposeRepresentation[C3,RootFromLevel[C3,3]][Irrep[C3][#]⊗Irrep[C3][{0,1,2}]]&/@AlcoveWeights[C3,RootFromLevel[C3,3]]//TableForm

Irrep[C3][#]->SteinbergDecomposeRepresentation[C3,RootFromLevel[C3,3]][Irrep[C3][#]⊗Irrep[C3][{0,0,3}]]&/@AlcoveWeights[C3,RootFromLevel[C3,3]]//TableForm

Irrep[C3][#]->SteinbergDecomposeRepresentation[C3,RootFromLevel[C3,3]][((Irrep[C3][#])^(⊗2))]&/@AlcoveWeights[C3,RootFromLevel[C3,3]]//TableForm

Irrep[C3][#]->N[qDimension[C3][Irrep[C3][#]]/.q->Exp[2π I/RootFromLevel[C3,3]]]&/@AlcoveWeights[C3,RootFromLevel[C3,3]]//TableForm

RootFromLevel[C3,3]

N@(qDimension[G2][Irrep[G2][{1,2}]]/.q->Exp[3 2π I/RootFromLevel[G2,2/3]])

N@(qDimension[C3][Irrep[C3][{1,0,0}]]/.q->Exp[2π I/RootFromLevel[C3,3]])

Simplify[(qDimension[G2][Irrep[G2][{1,2}]]/.q->Exp[3 2π I/RootFromLevel[G2,2/3]])-(qDimension[C3][Irrep[C3][{1,0,0}]]/.q->Exp[2π I/RootFromLevel[C3,3]])]

TwistFactor[G2,Irrep[(Subscript[G, 2])][{1,2}]]

TwistFactor[G2,Irrep[(Subscript[G, 2])][{0,0}]]

TwistFactor[G2,Irrep[(Subscript[G, 2])][{0,1}]]

TwistFactor[G2,Irrep[(Subscript[G, 2])][{0,2}]]

N@((q^6)+(q^8)/.q->Exp[2π I/28])

N@((q^12)+(q^2)/.q->Exp[-11 2π I/28])

SteinbergDecomposeRepresentation[G2,RootFromLevel[G2,2/3]][((Irrep[G2][{1,2}])^(⊗2))]

TwistFactor[G2,Irrep[(Subscript[G, 2])][{1,2}]]/.q->Exp[3 2π I/RootFromLevel[G2,2/3]]

PositiveRoots[C3]

TwistFactor[C3,Irrep[C3][{1,0,0}]]

TwistFactor[C3,Irrep[C3][{0,1,0}]]

TwistFactor[C3,Irrep[C3][{2,0,0}]]

RootFromLevel[C3,3]

TwistFactor[C3,Irrep[C3][{1,0,0}]]/.q->Exp[2π I/RootFromLevel[C3,3]]

TwistFactor[C3,Irrep[C3][{0,1,2}]]

TwistFactor[C3,Irrep[C3][{0,1,2}]]/.q->Exp[2π I/RootFromLevel[C3,3]]

TwistFactor[C3,Irrep[C3][{0,0,3}]]

TwistFactor[C3,Irrep[C3][{0,0,3}]]/.q->Exp[2π I/RootFromLevel[C3,3]]

SteinbergDecomposeRepresentation[C3,RootFromLevel[C3,3]][((Irrep[C3][{1,0,0}])^(⊗2))]

SteinbergDecomposeRepresentation[C3,RootFromLevel[C3,3]][((Irrep[C3][{0,1,2}])^(⊗2))]

Eigenvalues[BraidingMap[C3,Irrep[C3][{1,0,0}]⊗Irrep[C3][{1,0,0}],FundamentalBasis][{0,0,0}]//MatrixData]

Eigenvalues[BraidingMap[C3,Irrep[C3][{0,1,2}]⊗Irrep[C3][{0,1,2}],FundamentalBasis][{0,0,0}]//MatrixData]

TwistFactor[C3,Irrep[C3][{1,0,0}]]

TwistFactor[C3,Irrep[C3][{0,1,0}]]

TwistFactor[C3,Irrep[C3][{2,0,0}]]

DebugSet[True]

BraidingMap[G2,Irrep[(Subscript[G, 2])][{1,2}]⊗Irrep[(Subscript[G, 2])][{1,2}],FundamentalBasis]

Eigenvalues[BraidingMap[G2,Irrep[(Subscript[G, 2])][{1,2}]⊗Irrep[(Subscript[G, 2])][{1,2}],FundamentalBasis][{0,0}]//MatrixData]

Subcategory[Γ_,k_,V_]:=FixedPoint[Union[Flatten[Map[Function[W,SteinbergDecomposeRepresentation[Γ,RootFromLevel[Γ,k]][W⊗V]],#]/.d_DirectSum:>List@@d]~Join~#]&,{V}]

With[{Γ=C3,k=3,V=Irrep[C3][{1,0,0}]},Union[Flatten[Map[Function[W,SteinbergDecomposeRepresentation[Γ,RootFromLevel[Γ,k]][W⊗V]],#]/.d_DirectSum:>List@@d]]&[{V}]]

With[{Γ=C3,k=3,V=Irrep[C3][{1,0,0}]},Union[Flatten[Map[Function[W,SteinbergDecomposeRepresentation[Γ,RootFromLevel[Γ,k]][W⊗V]],#]/.d_DirectSum:>List@@d]]&[%]]

Subcategory[C3,3,Irrep[C3][{0,1,2}]]

Subcategory[C3,3,Irrep[C3][{1,0,0}]]

{{#},{Subcategory[C3,3,Irrep[C3][#]]}}&/@AlcoveWeights[C3,RootFromLevel[C3,3]]//TableForm