Volume computation for polytopes and partition functions for classical root systems

Abstract

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.Comment: 55 pages, 14 figures. Maple programs available at http://www.math.polytechnique.fr/~vergne/work/IntegralPoints.htm