Standard paths and standard monomials fixed by a diagram automorphism
type: Item
instance of: scholarly article
title: Standard paths and standard monomials fixed by a diagram automorphism
zbMATH Open document ID: 1023.17018
author: Satoshi Naito
author: Daisuke Sagaki
published in: Journal of Algebra
publication date: 2002-09-08T00:00:00Z
review text: Let \(\mathfrak{g}\) be a Kac-Moody algebra with symmetrizable generalized Cartan matrix (GCM) and \(\omega\) an automorphism of \(\mathfrak{g}\) induced by a Dynkin diagram automorphism. To such a \(\mathfrak{g}\) and \(\omega\) there can be associated another Kac-Moody algebra denoted \(\breve{\mathfrak{g}}\) and called the orbit Lie algebra of \(\mathfrak{g}\). The paper shows that the standard paths and the standard monomials fixed by a diagram automorphism of \(\mathfrak{g}\) can be identified with the standard paths and the standard monomials for \(\breve{\mathfrak{g}}\). This enables the authors to give a combinatorial proof of twining character formulas for an integrable highest weight module and for a Demazure module.
reviewed by: Stefano Capparelli
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 1797483
zbMATH Keywords: Kac-Moody algebras
zbMATH Keywords: standard paths
zbMATH Keywords: standard monomials
MaRDI profile type: Publication
full work available at URL: jabr.2001.9135
OpenAlex ID: W1980739274
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DOI: 10.1006/JABR.2001.9135
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description: scientific article; zbMATH DE number 1797483