A decomposition theorem for Demazure crystals.
type: Item
instance of: scholarly article
title: A decomposition theorem for Demazure crystals.
zbMATH Open document ID: 1100.17009
DOI: 10.1016/S0021-8693(03)00028-0
author: Anthony Joseph
published in: Journal of Algebra
publication date: 2003-08-13T00:00:00Z
review text: Let \(\mathfrak g\) be a symmetrizable Kac-Moody Lie algebra. In [Ann. Sci. Éc. Norm. Supér. (4) 18, No. 3, 389--419 (1985; Zbl 0589.22014)], Section 5.8, the author raised the question whether the tensor product of an integrable module with a Demazure module admits a filtration whose quotients are Demazure modules. The interest lies in the fact that one could then use the Demazure expression to compute multiplicities. This has been studied by various researchers. In this paper, the author addresses the crystal version of this problem in a purely combinatorial fashion. A new result is a computationally effective manner of obtaining multiplicities. Combined with the Demazure character formula he obtains some combinatorial identities.
reviewed by: Stefano Capparelli
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 1963608
zbMATH Keywords: Crystals
zbMATH Keywords: Demazure modules
MaRDI profile type: Publication
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full work available at URL: s0021-8693(03)00028-0
OpenAlex ID: W2074286576
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description: scientific article; zbMATH DE number 1963608