Denominator identities for Lie superalgebras

11/09/2010 - 12:15pm
11/09/2010 - 1:10pm
Shifra Reif (Weizmann Institute of Science)

In 1972 Macdonald generalized the Weyl denominator identity to affine root systems. The simplest example of these identities turned out to be the famous Jacobi triple product identity. In 1994 V. G. Kac and M. Wakimoto stated an analog for some affine Lie superalgebras and showed that it has applications in number theory. We provide identities for the rest of the (non-twisted) affine Lie superalgebras and deduce the Jacobi formula for counting the number of presentations of an integer as a sum of 8 squares (joint with M. Gorelik).

Millikan 208 (Pomona College)