Vector partition function and representation theory

We apply some recent developments of Baldoni-Beck-Cochet-Vergne on vector partition function, to Kostant’s and Steinberg’s formulae, for classical Lie algebras $A\mathrm{\_}r$, $B\mathrm{\_}r$, $C\mathrm{\_}r$, $D\mathrm{\_}r$. We therefore get efficient {\tt Maple} programs that compute for these Lie algebras: the multiplicity of a weight in an irreducible finite-dimensional representation; the decomposition coefficients of the tensor product of two irreducible finite-dimensional representations. These programs can also calculate associated Ehrhart quasipolynomials.