I'm pretty sure many a mathematician has longed for such a tool but I wasn't able to find such a question here, so here we go.
Is there, by any chance, an existing package or program that allows one to conveniently carry out explicit computations in finite-dimensional irreps of classical Lie algebras in terms of the action of the universal enveloping algebra?
To be more specific, the task I have at hand right now is to check whether the set of vectors obtained from the HWV by the action of certain elements of the UEA comprises a basis in the representation.
As far as I can tell, the software I've been able to find (such as LiE and LieART) does not provide such functionality.
KnotTheory
package available from katlas.org. I'm happy to answer questions by email. If the representations are at all large (dimension > 30, say) it starts to struggle. $\endgroup$