Denominator formulas for superalgebras

The Weyl denominator identity is one of the most intriguing identities in the character ring of a complex finite dimensional simple Lie algebra. In this talk we are presenting expressions for the analog of the denominator identity in the case of a basic classical Lie superalgebra. Unlike the Lie algebra case, the denominator identity depends on the choice of the positive system. Kac and Gorelik provided formulas for a special class of positive systems. In our talk we will explore a case that is opposite to the ones studied by Kac and Gorelik: the so called distinguished case. Connections with Howe theory of dual pairs are also made.