The crystal base and Littelmann's refined Demazure character formula
type: Item
instance of: scholarly article
title: The crystal base and Littelmann's refined Demazure character formula
zbMATH Open document ID: 0794.17008
DOI: 10.1215/S0012-7094-93-07131-1
author: Masaki Kashiwara
published in: Duke Mathematical Journal
publication date: 1994-09-08T00:00:00Z
review text: Demazure's character formula describes the weight multiplicities of the \(U({\mathfrak n}^ +)\)-module generated by an extremal vector of the irreducible highest weight \(U({\mathfrak g})\)-module, where \({\mathfrak g}\) is a symmetrizable Kac-Moody Lie algebra. In his paper [Crystal graphs and Young tableaux (preprint)], \textit{P. Littelmann} gives a conjecture of a generalization of the Demazure character formula which is described by crystal bases. In this paper the author proves this conjecture for any symmetrizable case.
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 558988
zbMATH Keywords: weight multiplicities
zbMATH Keywords: symmetrizable Kac-Moody Lie algebra
zbMATH Keywords: Demazure character formula
zbMATH Keywords: crystal bases
MaRDI profile type: Publication
cites work: Schubert varieties and Demazure's character formula
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cites work: Demazure character formula in arbitrary Kac-Moody setting
cites work: Projective normality of flag varieties and Schubert varieties
full work available at URL: s0012-7094-93-07131-1
OpenAlex ID: W1511084141
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description: scientific article; zbMATH DE number 558988