Dirac Cohomology for Lie Superalgebras

Abstract

The Dirac operators discussed so far were all associated to nondegenerate symmetric bilinear forms on subspaces of reductive Lie algebras and the Clifford algebras corresponding to these symmetric forms. The Dirac operator to be defined in this chapter is associated to a symplectic form on the odd part of a Lie superalgebra and the corresponding Weyl algebra. In [HP3] we obtain an analog of Vogan’s conjecture for this Dirac operator. Our results build upon the results of [Ko6].