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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HUANG, JS., WONG, K.D. A CASSELMAN–OSBORNE THEOREM FOR RATIONAL CHEREDNIK ALGEBRAS. Transformation Groups 23, 75–99 (2018). https://doi.org/10.1007/s00031-017-9441-x
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DOI: https://doi.org/10.1007/s00031-017-9441-x