Dear Andrew, The irreducible modules are constructed as quotients U(N)/I, where U(N) is a universal enveloping algebra, and I a left ideal. The algorithm is a kind of Groebner basis method, and the basis that comes out consists of the "normal" monomials modulo I. So it is not a particular type of basis. (The only thing that one can say is that it consists of weight vectors.)
The package SLA (http://science.unitn.it/~degraaf/sla.html) contains a function for computing a basis of an irreducible module that is also a basis of an admissible lattice. Best wishes, Willem de Graaf
Hello, I would like to know what basis GAP uses for irreducible representations of simple Lie algebras. Thank you!
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