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A Casselman-Osborne theorem for rational Cherednik algebras (1511.07965v2)
Published 25 Nov 2015 in math.RT
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.
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