Kostant partition functions for affine Kac-Moody algebras
type: Item
instance of: scholarly article
title: Kostant partition functions for affine Kac-Moody algebras
zbMATH Open document ID: 0881.17023
DOI: 10.1155/S0161171297000732
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1997-11-01T00:00:00Z
full work available at URL: https://eudml.org/doc/47796
review text: It is well-known from the theory of Kac-Moody algebras that multiplicities of weights of representations of Kac-Moody algebras can be expressed by means of multiplicity formula containing Kostant partition functions similar to one for finite dimensional representations of finite dimensional semisimple Lie algebras. Employing the method of generating functions in conjunction with various number-theoretical identities (Euler identity, Jacobi's triple and quintuple product identities, Tannery-Molk identity) the authors derive recursive relations for the Kostant partition functions for the affine Kac-Moody algebras. The partition functions for higher rank algebras are expressed in terms of the partition functions for the Kac-Moody algebra \(\widehat{\text{sl}}(2)\). Using the equivalence of these results with the expressions derived in some other papers, the authors obtain certain number-theoretical identities.
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 11F22
zbMATH DE Number: 1054261
zbMATH Keywords: multiplicity of weight
zbMATH Keywords: Kostant partition function
zbMATH Keywords: affine Kac-Moody algebra
author: T. S. Santhanam
author: R. Chakrabarti
reviewed by: A. U. Klimyk
MaRDI profile type: Publication
OpenAlex ID: W2135725021
description: scientific article; zbMATH DE number 1054261