Twining characters and Kostant's homology formula.
type: Item
instance of: scholarly article
title: Twining characters and Kostant's homology formula.
zbMATH Open document ID: 1058.17015
author: Satoshi Naito
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2003-12-15T00:00:00Z
review text: Twining characters of highest weight modules over a symmetrizable generalized Kac-Moody algebra \(\mathfrak{g}\) were introduced in [\textit{J. Fuchs, B. Schellekens} and \textit{C. Schweigert}, Commun. Math. Phys. 180, No. 1, 39--97 (1996; Zbl 0863.17020)]. These characters correspond to automorphisms of Dynkin diagrams. In the paper under review the author uses an extension (to generalized Kac-Moody algebras) of Kostant's homology formula to obtain a formula for twining characters of the homology modules \(H_j(\mathfrak{n}_-,L(\Lambda))\) of the negative part \(\mathfrak{n}_-\) of \(\mathfrak{g}\) with coefficients in some irreducible highest weight module \(L(\Lambda)\). This result is used to obtain a new proof of the formula for the twining character of \(L(\Lambda)\) in the case when \(\Lambda\) is symmetric dominant and integral. This new proof reveals the role, which is played by the subgroup \(\tilde{W}\) of the Weyl group, which consists of all elements, commuting with the Dynkin diagram automorphisms.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B55
zbMATH DE Number: 1998364
zbMATH Keywords: Kac-Moody algebra
zbMATH Keywords: Verma module
zbMATH Keywords: highest weight
zbMATH Keywords: homology
zbMATH Keywords: simple module
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1113246936
OpenAlex ID: W2035614802
cites work: Generalized Kac-Moody algebras
cites work: Some automorphisms of generalized Kac-Moody algebras
cites work: From Dynkin diagram symmetries to fixed point structures
cites work: Lie algebra homology and the Macdonald-Kac formulas
cites work: Q4040877
cites work: Q3027260
cites work: Graded Lie superalgebras, supertrace formula, and orbit Lie superalgebras.
cites work: Kostant's formula for a certian class of generalized Kac-Moody algebras
cites work: The strong Bernstein-Gelfand-Gelfand resolution for generalized Kac-Moody algebras. I: The existence of the resolution
cites work: The strong Bernstein-Gelfand-Gelfand resolution for generalized Kac-Moody algebras. II: An explicit construction of the resolution
cites work: Q4547423
DOI: 10.2748/TMJ/1113246936
description: scientific article; zbMATH DE number 1998364