Some new generating functions for weight multiplicities (Q1897540)

For each complex semisimple Lie algebra, the author introduces a generating function of formal characters of simple modules. Then using Weyl's character formula and the computation of residues he obtains a formula for weight multiplicities. Explicit computations are carried out for Lie algebras of type \(A_2\), \(B_2\), and \(G_2\). Some of these computations are done by means of a computer software package. It seems very likely to extend the computations to algebras of higher rank.