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arXiv · 0804.2356

Continuous crystals and Duistermaat-Heckman measure for Coxeter groups

Philippe Biane·Philippe Bougerol·Neil O'Connell
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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.

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Philippe Biane, Philippe Bougerol, Neil O'Connell. 2009-01-14. Continuous crystals and Duistermaat-Heckman measure for Coxeter groups. https://doi.org/10.1016/j.aim.2009.02.016

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