Continuous crystals and Duistermaat-Heckman measure for Coxeter groups

Details Continuous crystals and Duistermaat-Heckman measure for Coxeter groups Continuous crystals and Duistermaat-Heckman measure for Coxeter groups

2008-04-15

arxiv.org/abs/0804.2356v2

Mathematics

Representation Theory

Scientific paper

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.

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