Polytope sums and Lie characters

Details Polytope sums and Lie characters Polytope sums and Lie characters

2004-05-06

arxiv.org/abs/math-ph/0405016v1

published in 'Symmetry in Physics - in Memory of Robert T. Sharp', ed. P. Winternitz et al (AMS, 2004)

Physics

Mathematical Physics

13 pages, 0 figures

Scientific paper

A new application of polytope theory to Lie theory is presented. Exponential
sums of convex lattice polytopes are applied to the characters of irreducible
representations of simple Lie algebras. The Brion formula is used to write a
polytope expansion of a Lie character, that makes more transparent certain
degeneracies of weight-multiplicities beyond those explained by Weyl symmetry.

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