[GAP Forum] Basis for irreducible representations

[degraaf at science.unitn.it]

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!