Vector partition function and representation theory

Details Vector partition function and representation theory Vector partition function and representation theory

2005-06-09

arxiv.org/abs/math/0506159v1

Mathematics

Representation Theory

Accepted for software demonstration during FPSAC 2005 (Taormina, Italy). 12 pages

Scientific paper

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 $A\_r$, $B\_r$, $C\_r$, $D\_r$. 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.

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