Biane, Philippe, Bougerol, Philippe and O'Connell, Neil (2009) Continuous crystal and Duistermaat-Heckman measure for Coxeter groups. Advances in Mathematics, Vol.221 (No.5). pp. 1522-1583. doi:10.1016/j.aim.2009.02.016 ISSN 0001-8708.

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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 explore their main properties in the case of finite Coxeter groups, where we use a generalization of the Littelmann path model to show the existence of the crystals. We introduce a remarkable measure, analogous to the 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. (C) 2009 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Advances in Mathematics
Publisher:	Academic Press
ISSN:	0001-8708
Official Date:	1 August 2009
Dates:	Date Event 1 August 2009 Published
Volume:	Vol.221
Number:	No.5
Number of Pages:	62
Page Range:	pp. 1522-1583
DOI:	10.1016/j.aim.2009.02.016
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Science Foundation Ireland
Grant number:	SFI04/RP1/1512

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