A Casselman-Osborne theorem for rational Cherednik algebras

Abstract

We define Lie algebra cohomology associated with the half-Dirac operators for representations of rational Cherednik algebras and show that it has property described in the Casselman-Osborne Theorem by establishing a version of the Vogan's conjecture for the half-Dirac operators. Moreover, we study the relationship between Lie algebra cohomology and Dirac cohomology in analogy of the representations for semisimple Lie algebras.

To appear in Transformation Groups

References in corpus (2)

• Characters of Springer representations on elliptic conjugacy classes
• Dirac operators and Lie algebra cohomology