Modular transformations of SU(N) affine characters and their commutant
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.
characters of integrable representations
scientific article; zbMATH DE number 4152655
scientific article