Abstract:

In 1972 I.G. Macdonald generalized a classical formula of H. Weyl, obtaining, in particular, a formula for certain powers of the eta-function which include some classical identities of Jacobi. In 1994 V. Kac and M. Wakimoto conjectured a super-analogue of Macdonald identities and proved it for some special cases. Specializations of these identities give, in particular, Jacobi and Legendre formulas for representing an integer as a sum of squares or a sum of triangular numbers, respectively. In this talk I will outline several approaches to Macdonald identities, in particular, a new one, which leads to a proof of Kac-Wakimoto formulas.