Continuous crystals and Duistermaat-Heckman measure for Coxeter groups
Representation Theory
2013-07-15 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0804.2356,
title = {Continuous crystals and Duistermaat-Heckman measure for Coxeter groups},
author = {Philippe Biane and Philippe Bougerol and Neil O'Connell},
journal= {arXiv preprint arXiv:0804.2356},
year = {2013}
}