Modular transformations of SU(N) affine characters and their commutant
type: Item
instance of: scholarly article
title: Modular transformations of SU(N) affine characters and their commutant
zbMATH Open document ID: 0703.17017
DOI: 10.1007/BF02104506
published in: Communications in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: The authors examine the action of the modular group on the characters of integrable representations of the Kac-Moody algebra associated to SU(N). Let S and T denote the generators of the modular group, a basis of the algebra of matrices commuting with S and T is described by orbits under the modular action on \(G_ n\times G_ n\), where \(G_ n\) denotes a quotient of the weight lattice of SU(N). It is proved that there is a basis consisting of matrices with integral entries, i.e. a basis of the subalgebra over the rationals of the commutant of S and T. The case \(N=3\) is discussed in some detail by use of an interpretation of the weight lattice as a quadratic field.
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 81T25
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 4152655
zbMATH Keywords: modular group
zbMATH Keywords: characters of integrable representations
zbMATH Keywords: Kac-Moody algebra
author: Michel Bauer
author: C. Itzykson
reviewed by: Helmut Boseck
MaRDI profile type: Publication
cites work: Q3693672
cites work: The A-D-E classification of minimal and \(A_ 1^{(1)}\) conformal invariant theories
cites work: GN ⊗ GL/GN+L CONFORMAL FIELD THEORIES AND THEIR MODULAR INVARIANT PARTITION FUNCTIONS
cites work: Classical and quantum conformal field theory
Recommended article: Q3973927
Recommended article: Q3203194
Recommended article: Modular invariance of characters of vertex operator algebras
Recommended article: Q4497343
Recommended article: The classification of affine \(SU(3)\) modular invariant partition functions
Recommended article: Characters of (relatively) integrable modules over affine Lie superalgebras
Recommended article: Q3202275
Recommended article: Dimension of the commutant for the SU(N) affine algebras
Recommended article: Modular and conformal invariance constraints in representation theory of affine algebras
Recommended article: A module-theoretic interpretation of some character formula
description: scientific article; zbMATH DE number 4152655