The branching rules for affine Lie algebras
type: Item
instance of: scholarly article
title: The branching rules for affine Lie algebras
zbMATH Open document ID: 0811.17027
author: Shirong Lu
published in: Advances in Mathematics
publication date: 1994-08-17T00:00:00Z
full work available at URL: http://hdl.handle.net/2027.42/31650
review text: The irreducible highest weight representations of affine Kac-Moody algebras are one of the main tools in the construction of conformal field theories. One of the good clues to the understanding of the structure of irreducible highest weight representations of affine Kac-Moody algebras is to calculate the string functions, which count the weight multiplicities. The problem of determining the string functions of all level one modules for \(C^{(1)}_ l\) was stated as an open problem in \textit{V. G. Kac's} book [Infinite dimensional Lie algebras, 3rd ed., Cambridge University Press (1990; Zbl 0716.17022)]. In 1988, a formula for this was discovered by \textit{V. G. Kac} and \textit{M. Wakimoto} in terms of Virasoro characters [Adv. Math. 70, 156-236 (1988; Zbl 0661.17016)]. In this paper, the author gives a new formula for the string functions of all level one modules for \(C^{(1)}_ l\), which is expressed in terms of quadratic theta functions of degree \(l - 1\). Comparing his formula with the one obtained by Kac and Wakimoto, some curious theta function identities are discovered. He also finds a general formula expressing general branching functions in terms of string functions. As an application, the branching functions for the complementary decompositions are explicitly computed.
reviewed by: Seok-Jin Kang
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 611199
zbMATH Keywords: branching rules
zbMATH Keywords: irreducible highest weight representations
zbMATH Keywords: affine Kac- Moody algebras
zbMATH Keywords: conformal field theories
zbMATH Keywords: string functions
zbMATH Keywords: level one modules
zbMATH Keywords: theta function identities
zbMATH Keywords: branching functions
MaRDI profile type: Publication
OpenAlex ID: W1992638844
DOI: 10.1006/AIMA.1994.1038
description: scientific article; zbMATH DE number 611199