Denominator formulas for Lie superalgebras (extended abstract)

International audience We provide formulas for the Weyl-Kac denominator and superdenominator of a basic classical Lie superalgebra for a distinguished set of positive roots. \par Nous donnons les formules pour les dénominateurs et super-dénominateurs de Weyl-Kac d'une super-algèbre de Lie basique classique pour un ensemble distingué de racines positives.

Polynomial identities for simple Lie superalgebras

Polynomial identities for the generators of a simple basic classical Lie superalgebra are derived in arbitrary representations generated by a maximal (or minimal) weight vector. The infinitesimal characters occurring in the tensor product of two finite dimensional irreducible representations are also determined.