Dear gap-forum,
Is the naming convention for the basis of highest weight modules described
anywhere?
For example :
gap>L:=SimpleLieAlgebra("A",2,Rationals);;
gap>M1:=HighestWeightModule(L,[1,0]);;
gap>B1:=Basis(M1);;
gap>M2:=TensorProductOfAlgebraModules(M1,M1);;
gap>B2:=Basis(M2);;
gap> BasisVectors(B1);
[ 1*v0, y1*v0, y3*v0 ]
gap> BasisVectors(B2);
[ 1*(1*v0<x>1*v0), 1*(1*v0<x>y1*v0), 1*(1*v0<x>y3*v0), 1*(y1*v0<x>1*v0),
1*(y1*v0<x>y1*v0), 1*(y1*v0<x>y3*v0),
1*(y3*v0<x>1*v0), 1*(y3*v0<x>y1*v0), 1*(y3*v0<x>y3*v0) ]
1*v0,y1*v0,y3*v0 seems an odd choice without knowing where it came from.
Thanks,
r.n.
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