KnotTheoryPathScott = "c:\\scott\\projects\\KnotTheory\\trunk\\";
KnotTheoryPathEmily="/Users/emilypeters/Documents/Math/Knot Theory/trunk";
AppendTo[$Path, KnotTheoryPathScott];
AppendTo[$Path, KnotTheoryPathEmily];
<< KnotTheory`

QuantumGroupsDataDirectory[]="c:\\scott\\projects\\QuantumGroups\\trunk\\data";
AppendTo[$Path,QuantumGroupsDataDirectory[]];

wts2=Flatten[Outer[Plus,IdentityMatrix[6],IdentityMatrix[6],1],1]

qdims=qDimension[D6][Irrep[D6][#]]&/@IdentityMatrix[6]

Print[qDimension[D6][Irrep[D6][#]]]&/@wts2

qdims2=qDimension[D6][Irrep[D6][#]]&/@wts2;

N[((1+(Sqrt[5]))/2)]

Table[Chop[N[qdims/.q->(E^(2π I/k))]],{k,1,50}]//TableForm

Transpose[Table[Chop[N[qdims2/.q->(E^(2π I/k))]],{k,1,50}]]//TableForm

wts=Flatten[With[{n=2},Table[{i,j,k},{i,0,n},{j,0,n-i},{k,0,n-i-j}]],2]

Table[Table[Chop[N[qDimension[A1][Irrep[A1][{λ}]]/.q->(E^(2π I/k))]],{λ,0,10}],{k,4,20,2}]//TableForm

wts

qdims=qDimension[A3][Irrep[A3][#]]&/@wts

Table[Chop[N[qdims/.q->(E^(2π I/k))]],{k,1,20}]//TableForm

wts=Flatten[With[{n=2},Table[{i,j},{i,0,n},{j,0,n-i}]],1]

qdims=qDimension[A2][Irrep[A2][#]]&/@wts

Table[Chop[N[qdims/.q->(E^(2π I/k))]],{k,1,20}]//TableForm

N[{qDimension[A2][Irrep[A2][{1,0}]],qDimension[A1][Irrep[A1][{1}]]}/.q->(E^(2π I/10))]

N[{qDimension[A3][Irrep[A3][{1,0,0}]],qDimension[A1][Irrep[A1][{1}]]}/.q->(E^(2π I/12))]

N[{qDimension[A4][Irrep[A4][{1,0,0,0}]],qDimension[A1][Irrep[A1][{1}]]}/.q->(E^(2π I/14))]

Table[Chop[N[qDimension[A2][Irrep[A2][{1,0}]]/.q->(E^(2π I/k))]],{k,1,30}]

Table[Chop[N[qDimension[A3][Irrep[A3][{1,0,0}]]/.q->(E^(2π I/k))]],{k,1,20}]

Intersection[%%,%]

Table[Chop[N[qDimension[A4][Irrep[A4][{1,0,0,0}]]/.q->(E^(2π I/k))]],{k,1,20}]

Chop[N[Table[{qDimension[(Subscript[A, n])][Irrep[(Subscript[A, n])][UnitVector[n,1]]],qDimension[(Subscript[A, k])][Irrep[(Subscript[A, k])][UnitVector[k,1]]]}/.q->(E^(2π I/(2n+2k+4))),{n,1,8},{k,1,8}]]]

N[%]

d[n_]:=d[n]=Chop[N[(1/2)qDimension[A1][Irrep[A1][{2n-2}]]/.q->(E^(2π I/(8n-4)))]]

Table[Chop[N[(1/2)qDimension[A1][Irrep[A1][{2n-2}]]/.q->(E^(2π I/(8n-4)))]],{n,2,12}]

DualCoxeterNumber[A2]

DualCoxeterNumber[A1]

With[{Γ=A1},Table[Chop[N[qDimension[Γ][Irrep[Γ][#]]&/@IdentityMatrix[Rank[Γ]]/.q->(E^(2π I/k))]],{k,2DualCoxeterNumber[Γ]+2,2DualCoxeterNumber[Γ]+20}]]//TableForm

Clear[RepresentationsWithDimension]
RepresentationsWithDimension[x_]:={}

record[Γ_,V_,k_]:=Module[{d=Chop[N[qDimension[Γ][V]/.q->(E^(2π I/k))]]},
If[d>0,
RepresentationsWithDimension[d]=Union[RepresentationsWithDimension[d],{{V,k}}]
]
]

Table[record[A1,Irrep[A1][{λ}],k],{k,1,100},{λ,1,10}];

With[{Γ=D7},Table[record[Γ,Irrep[Γ][#],k]&/@IdentityMatrix[Rank[Γ]],{k,1,50}]]

RepresentationsWithDimension[d[2]]

RepresentationsWithDimension[d[3]]

RepresentationsWithDimension[d[4]]

RepresentationsWithDimension[d[5]]

RepresentationsWithDimension[d[6]]

RepresentationsWithDimension[d[7]]

RepresentationsWithDimension[d[8]]

d[8]

N[qDimension[D7][Irrep[D7][{0,0,0,0,0,0,1}]]/.q->(E^(2π I/30))]

d[9]

N[qDimension[D8][Irrep[D8][{0,0,0,0,0,0,0,1}]]/.q->(E^(2π I/34))]

RepresentationsWithDimension[d[9]]

DualCoxeterNumber[A1]

With[{Γ=A1},Table[Chop[N[qDimension[Γ][Irrep[Γ][#]]&/@(2IdentityMatrix[Rank[Γ]])/.q->(E^(2π I/k))]],{k,2DualCoxeterNumber[Γ]+2,2DualCoxeterNumber[Γ]+40}]]//TableForm

With[{Γ=A2},Table[Chop[N[qDimension[Γ][Irrep[Γ][#]]&/@IdentityMatrix[Rank[Γ]]/.q->(E^(2π I/k))]],{k,2DualCoxeterNumber[Γ]+2,2DualCoxeterNumber[Γ]+50}]]//TableForm

With[{Γ=A3},Table[Chop[N[qDimension[Γ][Irrep[Γ][#]]&/@IdentityMatrix[Rank[Γ]]/.q->(E^(2π I/k))]],{k,2DualCoxeterNumber[Γ]+2,2DualCoxeterNumber[Γ]+40}]]//TableForm

With[{Γ=A4},Table[Chop[N[qDimension[Γ][Irrep[Γ][#]]&/@IdentityMatrix[Rank[Γ]]/.q->(E^(2π I/k))]],{k,2DualCoxeterNumber[Γ]+2,2DualCoxeterNumber[Γ]+40}]]//TableForm

With[{Γ=D4},Table[Chop[N[qDimension[Γ][Irrep[Γ][#]]&/@IdentityMatrix[Rank[Γ]]/.q->(E^(2π I/k))]],{k,2DualCoxeterNumber[Γ]+2,2DualCoxeterNumber[Γ]+20}]]//TableForm

With[{Γ=D6},Table[Chop[N[qDimension[Γ][Irrep[Γ][#]]&/@IdentityMatrix[Rank[Γ]]/.q->(E^(2π I/k))]],{k,2DualCoxeterNumber[Γ]+2,2DualCoxeterNumber[Γ]+20}]]//TableForm

With[{Γ=D8},Table[Chop[N[qDimension[Γ][Irrep[Γ][#]]&/@IdentityMatrix[Rank[Γ]]/.q->(E^(2π I/k))]],{k,2DualCoxeterNumber[Γ]+2,2DualCoxeterNumber[Γ]+20}]]//TableForm