arXiv subjects
Publications and source records attributed to Charles Cochet.
This paper presents an algorithm to compute the value of the inverse Laplace transforms of rational functions with poles on arrangements of hyperplanes. As an application, we present an efficient computation of the partition function for classical root systems.
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.
We apply some recent developments of Baldoni-DeLoera-Vergne on vector partition functions, to Kostant and Steinberg formulas, in the case of $A_r$. We therefore get a fast {\sc Maple} program that computes for $A_r$: the multiplicity $c_{λ,μ}$ of the weight $μ$ in the representation $V(λ)$ of highest weight $λ$; the multiplicity $c_{λ,μ,ν}$ of the representation $V(ν)$ in $V(λ)\otimes V(μ)$. The computation also gives the locally polynomial functions $c_{λ,μ}$ and $c_{λ,μ,ν}$.