[GAP Forum] representations of Lie algebras

[R.N. Tsai]

I'm getting familiar with the facilities that GAP provides to work with
Lie algebras. I didn't find a way to get explicit matrices for representation.
Is this possible?
For example :
 Test:=function()local algebra,basis,rep,repbasis;
  algebra:=SimpleLieAlgebra("A",2,Rationals);Print(" algebra = ",algebra,"\n");
  basis:=ChevalleyBasis(algebra); 
  rep:= HighestWeightModule(algebra, [ 1,1] );
  repbasis:=Basis(rep);Print(" basis for rep = ",repbasis,"\n");
  return repbasis;
 end;
returns 
 Basis( <8-dimensional left-module over Algebra( Rationals, 
 [ v.1, v.2, v.3, v.4, v.5, v.6, v.7, v.8 ] )>, 
 [ 1*v0, y1*v0, y2*v0, y1*y2*v0, y3*v0, y1*y3*v0, y2*y3*v0, y3^(2)*v0 ] )
how would this be converted to a matrix representation for the generators
of the algebra.
Thanks,
r.n.

		
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