Dror Bar-Natan: Papers: WKO:

A^v in Degree 2

Pensieve Header: We analyze ${\mathcal A}^v$ in degree 2.

SetDirectory["C:/drorbn/AcademicPensieve/Projects/WKO"];
<< Dimensions.m

ShowMatrix[mat_] := MatrixForm[Prepend[mat,
diags /. Diag[ar[i_,j_],ar[k_,l_]] :> Column[{
1000i+100j+10k+l
}]
]]

Print[Diagrams[2 ar]]

diags={
Diag[ar[1,3],ar[4,2]],Diag[ar[2,4],ar[3,1]],Diag[ar[1,3],ar[2,4]],Diag[ar[3,1],ar[4,2]],
Diag[ar[1,4],ar[3,2]],Diag[ar[1,4],ar[2,3]],Diag[ar[2,3],ar[4,1]],Diag[ar[3,2],ar[4,1]],
Diag[ar[1,2],ar[3,4]],Diag[ar[2,1],ar[3,4]],Diag[ar[1,2],ar[4,3]],Diag[ar[2,1],ar[4,3]]
}

Diagrams[R6T]

rels = R /@ Diagrams[R6T]

mat = SparseArray[
Join @@ Table[
rel=rels[[i]];
{i,Position[diags, #][[1,1]]} -> Coefficient[rel, #]& /@ Cases[{rel}, diag_Diag, Infinity],
{i,Length[rels]}
],
{Length[rels], Length[diags]}
];

mat // ShowMatrix

ShowMatrix[RowReduce[mat]]

The following can only be executed after loading code from "AcademicPensieve/Projects/Arrow_Diagrams_and_gl(N)/Arrow_Diagrams_and_gl(N).nb":

Import["http://katlas.math.toronto.edu/drorbn/AcademicPensieve/Projects/Arrow_Diagrams_and_gl(N)/Arrow_Diagrams_and_gl(N).m"]

(# -> Wgl[#][n,k])& /@ diags