Vector partition function and representation theory

Charles Cochet (1)

1 IMJ - Institut de Mathématiques de Jussieu

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.

Mots clés: weight multiplicity; Littlewood-Richardson coefficients; Kostka numbers; Ehrhart quasipolynomial; convex polytopes; partition function

Domaines: Théorie des représentations [math.RT]; Combinatoire [math.CO]

Charles Cochet. Vector partition function and representation theory. 2005. ⟨hal-00005244⟩