Continuous crystals and Duistermaat-Heckman measure for Coxeter groups

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.

References in corpus (4)

• Littelmann paths and brownian paths
• Toric degenerations of spherical varieties
• The octahedron recurrence and gl(n) crystals
• A Pentagonal Crystal, the Golden Section, alcove packing and aperiodic tilings

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