%0 Journal Article
%T Continuous crystals and Duistermaat-Heckman measure for Coxeter groups
%A Philippe Biane
%A Philippe Bougerol
%A Neil O'Connell
%J Mathematics
%D 2008
%I arXiv
%R 10.1016/j.aim.2009.02.016
%X We introduce a notion of continuous crystal analogous, for general Coxeter groups, to the combinatorial crystals introduced by Kashiwara in representation theory of Lie algebras. We use a generalization of the Littelmann path model to show the existence of the crystals, and study an associated Duistermaat-Heckman measure, which we interpret in terms of Brownian motion. We also show that the Littelmann path operators can be derived from simple considerations on Sturm-Liouville equations.
%U http://arxiv.org/abs/0804.2356v2