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

LevelFromRoot[A3,14]

AlcoveWeights[A3,14]

Chop@N@Simplify[qDimension[A3][Irrep[A3][#]]/.q->Exp[((2π I)/14)]]&/@AlcoveWeights[A3,14]

dimension1=Cases[AlcoveWeights[A3,14],λ_/;FullSimplify[(qDimension[A3][Irrep[A3][λ]]/.q->Exp[((2π I)/14)])-1]==0]

RootReduce[ExpToTrig[qDimension[A3][Irrep[A3][#]]/.q->Exp[((2π I)/14)]]&/@dimension1]

RootReduce[ExpToTrig[qDimension[A3][Irrep[A3][#]]/.q->-Exp[((2π I)/14)]]&/@dimension1]

RootReduce[ExpToTrig[TwistFactor[A3,Irrep[A3][#]]/.q->Exp[((2π I)/14)]&/@dimension1]]

RootReduce[ExpToTrig[TwistFactor[A3,Irrep[A3][#]]/.q->Exp[-((2π I)/14)]&/@dimension1]]

RootReduce[ExpToTrig[TwistFactor[A3,Irrep[A3][#]]/.q->-Exp[((2π I)/14)]&/@dimension1]]

RootReduce[ExpToTrig[TwistFactor[A3,Irrep[A3][#]]/.q->-Exp[-((2π I)/14)]&/@dimension1]]

RootReduce[ExpToTrig[qDimension[A3][Irrep[A3][#]]/.q->-Exp[-((2π I)/14)]]]&/@dimension1

Outer[SteinbergDecomposeRepresentation[A3,14][Irrep[A3][#1]⊗Irrep[A3][#2]]&,dimension1,dimension1,1]//TableForm

Outer[SteinbergDecomposeRepresentation[A3,14][Irrep[A3][#1]⊗Irrep[A3][#2]]&,AlcoveWeights[A3,14],AlcoveWeights[A3,14],1]//TableForm

Rule@@@Outer[SteinbergDecomposeRepresentation[A3,14][Irrep[A3][#1]⊗Irrep[A3][#2]]&,AlcoveWeights[A3,14],{{0,0,0},{3,0,0}},1]

Cases[AlcoveWeights[A3,14],λ_/;Length[SteinbergDecomposeRepresentation[A3,14][Irrep[A3][λ]⊗Irrep[A3][λ]]]==3]

SteinbergDecomposeRepresentation[A3,14][Irrep[A3][#]⊗Irrep[A3][#]]&/@%

S={{0,0,0},{0,2,0},{1,0,1},{0,1,2},{2,1,0}};

Outer[SteinbergDecomposeRepresentation[A3,14][Irrep[A3][#1]⊗Irrep[A3][#2]]&,S,S,1]//TableForm