run "date";
needsPackage("LieAlgebraRepresentations");
sl6 = simpleLieAlgebra("A",5);
rhoStd = standardRepresentation(sl6);
rhoW2Std = exteriorPower(2,rhoStd);
rhoW2Stdstar = dual rhoW2Std;
-- Step 2: Get V11011 in W9W2Stdstar
V11011 = irreducibleLieAlgebraModule({1,1,0,1,1},sl6);
LAB = rhoStd#"Basis";
time L11011 = GTrepresentationMatrices(V11011);
rhoV11011 = lieAlgebraRepresentation(V11011,LAB,L11011);
-- Need a hwv for V11011 in W9W2Std
-- Relatively easy because the weight {1,1,0,1,1} subspace in W9W2Std is one-dimensional
wts = representationWeights(rhoW2Stdstar);
s9 = subsets(apply(#wts, i -> i),9);
t=first select(s9, s -> sum apply(s, j -> wts_j)=={1,1,0,1,1})
hwv = transpose matrix {apply(s9, s -> if s==t then 1/1 else 0/1)};
time V11011inW9W2Stdstar = VInWedgekW(rhoV11011,9,rhoW2Stdstar,hwv,"SaveAsFunction"=>"V11011inW9W2Stdstar");
-- Step 3: Get the invariant in V11011 otimes V11011
V00000inV11011otimesV11011 = gtInvariantInVtensorVdual({1,1,0,1,1});
fn = openOut "V00000inV11011otimesV11011.m2";
fn << "V00000inV11011otimesV11011 = (A,B) -> ";
fn << toString V00000inV11011otimesV11011 << endl;
close fn;
run "date";