Kostant partition functions for affine Kac-Moody algebras
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.
scientific article; zbMATH DE number 1054261