[GAP Forum] naming convention for basis of highest weight modules

[R.N. Tsai]

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.