Real characters for Demazure modules of rank two affine Lie algebras
type: Item
instance of: scholarly article
title: Real characters for Demazure modules of rank two affine Lie algebras
zbMATH Open document ID: 0873.17022
author: Yasmine Sanderson
published in: Journal of Algebra
publication date: 1997-10-30T00:00:00Z
review text: Let \({\mathfrak g}\) be a Kac-Moody algebra of type \(A_1^{(1)}\) or \(A_2^{(2)} \). Given a dominant weight \(\lambda\), let \(V(\lambda)\) denote the irreducible \({\mathfrak g}\)-module with heighest weight \(\lambda\). Given an element \(w\) of the Weyl group, let \(E_w (\lambda)\) denote the Demazure module associated to \(w\), namely, \(E_w (\lambda)\) is the \({\mathfrak b}\)-module generated by the weight space \(V_{w (\lambda)}\) (of dimension one), \({\mathfrak b}\) being the Borel subalgebra of \({\mathfrak g}\). For \(n\in \mathbb Z\), let \(E_w (\lambda)_n = \bigoplus_{\mu\in \lambda- n\alpha_0 +\mathbb Z \delta} E_w (\lambda)_\mu\), where \(\alpha_0, \delta\) have the usual meaning. In this paper, the author computes \(\chi_n (E_w (\lambda)): =\sum_{n\in \mathbb Z} \dim E_w (\lambda)_nq^n\) in an explicit way. Unlike the other known character formulae, namely the Kac-Weyl character formula and Demazure character formula, which involve massive cancellations, the formula given in this paper is positive-termed.
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 941276
zbMATH Keywords: path model
zbMATH Keywords: Kac-Moody algebra
zbMATH Keywords: heighest weight
zbMATH Keywords: Demazure module
zbMATH Keywords: character formulae
Wikidata QID: Q115396087
reviewed by: V. Lakshmibai
MaRDI profile type: Publication
full work available at URL: jabr.1996.0294
OpenAlex ID: W1976377573
DOI: 10.1006/JABR.1996.0294
description: scientific article; zbMATH DE number 941276