QuantumGroupsPath = "c:\\scott\\projects\\QuantumGroups\\trunk\\package\\";
AppendTo[$Path, QuantumGroupsPath];
<<QuantumGroups`

With[{T=A},Table[DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][2UnitVector[k,1]])^(⊗2))],{k,1,7}]]

N[1+(Sqrt[3])]

Min[Abs[Flatten[Table[Chop@N[(qDimension[(Subscript[A, k])][Irrep[(Subscript[A, k])][2UnitVector[k,1]]]/.q->(E^((2π I)/l)))-(1+(Sqrt[3]))],{k,8,10},{l,20,100}]]]]

Min[Abs[Flatten[Table[Chop@N[(qDimension[(Subscript[A, k])][Irrep[(Subscript[A, k])][2UnitVector[k,1]]]/.q->(E^((2π I)/l)))-(1+(Sqrt[3]))],{k,24,24},{l,20,100}]]]]

Table[Chop@N[(qDimension[(Subscript[A, k])][Irrep[(Subscript[A, k])][2UnitVector[k,1]]]/.q->(E^((2π I)/l)))-(1+(Sqrt[3]))],{k,25,25},{l,20,100}]

Table[Chop@N[(qDimension[(Subscript[A, k])][Irrep[(Subscript[A, k])][2UnitVector[k,1]]]/.q->(E^((2π I)/l)))-(1+(Sqrt[3]))],{k,20,20},{l,20,100}]

Table[Chop@N[(qDimension[(Subscript[A, k])][Irrep[(Subscript[A, k])][2UnitVector[k,1]]]/.q->(E^((2π I)/l)))-(1+(Sqrt[3]))],{k,13,13},{l,20,100}]

Table[Chop@N[(qDimension[(Subscript[A, k])][Irrep[(Subscript[A, k])][2UnitVector[k,1]]]/.q->(E^((2π I)/l)))-(1+(Sqrt[3]))],{k,8,8},{l,20,100}]

Length@AlcoveWeights[(Subscript[A, 20]),24]

Length@AlcoveWeights[(Subscript[A, 13]),24]

Length@AlcoveRoots[(Subscript[A, 8]),24]

Length@Cases[AlcoveWeights[(Subscript[A, 8]),24],λ_/;RootWeightQ[(Subscript[A, 8]),3λ]]

Length@AlcoveWeights[(Subscript[A, 8]),24]

Union[FullSimplify[qDimension[(Subscript[A, 8])][Irrep[(Subscript[A, 8])][#]]/.q->(E^((2π I)/24))]&/@AlcoveRoots[(Subscript[A, 8]),24]]

Union[FullSimplify[qDimension[(Subscript[A, 8])][Irrep[(Subscript[A, 8])][#]]/.q->(E^((2π I)/24))]&/@Cases[AlcoveWeights[(Subscript[A, 8]),24],λ_/;RootWeightQ[(Subscript[A, 8]),3λ]]]

Union[FullSimplify[qDimension[(Subscript[A, 8])][Irrep[(Subscript[A, 8])][#]]/.q->(E^((2π I)/24))]&/@AlcoveWeights[(Subscript[A, 8]),24]]

Table[Chop@N[(qDimension[(Subscript[A, k])][Irrep[(Subscript[A, k])][2UnitVector[k,1]]]/.q->(E^((2π I)/l)))-(1+(Sqrt[3]))],{k,1,7},{l,20,30}]

Chop@N[(qDimension[(Subscript[A, 1])][Irrep[(Subscript[A, 1])][2UnitVector[1,1]]]/.q->(E^((2π I)/24)))-(1+(Sqrt[3]))]

AlcoveWeights[(Subscript[A, 1])

With[{T=A},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][2UnitVector[k,1]])^(⊗2))],{k,1,7}]]

With[{T=B},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][2UnitVector[k,1]])^(⊗2))],{k,2,5}]]

With[{T=C},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][2UnitVector[k,1]])^(⊗2))],{k,3,5}]]

With[{T=D},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][2UnitVector[k,1]])^(⊗2))],{k,4,5}]]

Min[Abs[Flatten[Table[Chop@N[(qDimension[(Subscript[A, k])][Irrep[(Subscript[A, k])][UnitVector[k,2]]]/.q->(E^((2π I)/l)))-(1+(Sqrt[3]))],{k,15,20},{l,10,100}]]]]

Table[Chop@N[(qDimension[(Subscript[A, k])][Irrep[(Subscript[A, k])][UnitVector[k,2]]]/.q->(E^((2π I)/l)))-(1+(Sqrt[3]))],{k,19,19},{l,20,100}]

Table[Chop@N[(qDimension[(Subscript[A, k])][Irrep[(Subscript[A, k])][UnitVector[k,2]]]/.q->(E^((2π I)/l)))-(1+(Sqrt[3]))],{k,9,9},{l,20,30}]

Table[Chop@N[(qDimension[(Subscript[A, k])][Irrep[(Subscript[A, k])][UnitVector[k,2]]]/.q->(E^((2π I)/l)))-(1+(Sqrt[3]))],{k,2,2},{l,20,30}]

AlcoveWeights[(Subscript[A, 14]),24]

Length@AlcoveWeights[(Subscript[A, 14]),24]

FullSimplify[qDimension[(Subscript[A, 14])][Irrep[(Subscript[A, 14])][#]]/.q->(E^((2π I)/24))]&/@AlcoveWeights[(Subscript[A, 14]),24]

Length@AlcoveWeights[A9,24]

FullSimplify[qDimension[A9][Irrep[A9][#]]/.q->(E^((2π I)/24))]&/@AlcoveWeights[A9,24]

Union[%]

N[%]

AlcoveRoots[A9,24]

FullSimplify[qDimension[A9][Irrep[A9][#]]/.q->(E^((2π I)/24))]&/@Cases[AlcoveWeights[A9,24],λ_/;RootWeightQ[A9,2λ]]

FullSimplify[qDimension[A9][Irrep[A9][#]]/.q->(E^((2π I)/24))]&/@AlcoveRoots[A9,24]

AlcoveWeights[A2,24]

Simplify[qDimension[A2][Irrep[A2][#]]/.q->(E^((2π I)/24))]&/@AlcoveWeights[A2,24]

Union[%]

N[%]

Simplify[qDimension[A2][Irrep[A2][#]]/.q->(E^((2π I)/24))]&/@AlcoveRoots[A2,24]

N[Union[%]]

Simplify[(qDimension[(Subscript[A, 2])][Irrep[(Subscript[A, 2])][UnitVector[2,1]]]/.q->(E^((2π I)/24)))-(1+(Sqrt[3]))]

Simplify[(qDimension[(Subscript[A, 2])][Irrep[(Subscript[A, 2])][UnitVector[2,2]]]/.q->(E^((2π I)/24)))-(1+(Sqrt[3]))]

With[{T=A},Table[DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,2]])^(⊗2))],{k,2,7}]]

With[{T=A},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,2]])^(⊗2))],{k,2,7}]]

With[{T=B},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,2]])^(⊗2))],{k,2,6}]]

With[{T=C},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,2]])^(⊗2))],{k,3,6}]]

With[{T=D},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,2]])^(⊗2))],{k,4,6}]]

With[{T=A},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,1]+UnitVector[k,2]])^(⊗2))],{k,2,7}]]

With[{T=B},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,1]+UnitVector[k,2]])^(⊗2))],{k,2,6}]]

With[{T=C},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,1]+UnitVector[k,2]])^(⊗2))],{k,3,6}]]

With[{T=D},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,1]+UnitVector[k,2]])^(⊗2))],{k,4,6}]]

With[{T=A},Table[DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,3]])^(⊗2))],{k,3,9}]]

With[{T=A},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,3]])^(⊗2))],{k,3,9}]]

With[{T=B},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,3]])^(⊗2))],{k,3,6}]]

With[{T=C},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,3]])^(⊗2))],{k,3,7}]]

With[{T=D},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,3]])^(⊗2))],{k,5,7}]]

With[{T=A},Table[Length@DecomposeRepresentation[(Subscript[T, k])][((Irrep[(Subscript[T, k])][UnitVector[k,1]+UnitVector[k,k]])^(⊗2))],{k,1,9}]]