On Demazure polynomials
type: Item
instance of: scholarly article
title: On Demazure polynomials
zbMATH Open document ID: 1134.17012
author: Séverine Verneyre-Petitgirard
published in: Journal of Algebra
publication date: 2007-01-26T00:00:00Z
review text: For an affine Kac-Moody algebra \(\mathfrak g\), let \(\lambda\) be a dominant weight and \(w\) an element of the Weyl group. Denote by \(e_{w\lambda}\) an element of \(L(\lambda)_{w\lambda}\), where \(L(\lambda)\) is the unique irreducible \(\mathfrak g\)-module of highest weight \(\lambda\). The \(\mathfrak b\)-module generated by \(e_{w\lambda}\) is called the Demazure module denoted by \(E_w(\lambda)\), (\(\mathfrak b\) is the Borel subalgebra of \(\mathfrak g\)). The dimension of \(E_w(\lambda)\) is a polynomial in \(\lambda\). The author proves that this polynomial is harmonic. He also calculates explicitly all the Demazure polynomials for a subset \(\mathcal E\) of \(W\) in the case when \(\mathfrak g=\widehat{\mathfrak{sl}}\).
reviewed by: Stefano Capparelli
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 5118820
zbMATH Keywords: Lie algebra
zbMATH Keywords: Kac-Moody algebra
zbMATH Keywords: Demazure module
zbMATH Keywords: Demazure polynomials
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.07.002
OpenAlex ID: W1993766423
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DOI: 10.1016/J.JALGEBRA.2006.07.002
description: scientific article; zbMATH DE number 5118820