Transformation Groups

, Volume 23, Issue 1, pp 75–99 | Cite as

A CASSELMAN–OSBORNE THEOREM FOR RATIONAL CHEREDNIK ALGEBRAS

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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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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsHong Kong University of Science and TechnologyHong KongChina
  2. 2.Department of MathematicsCornell UniversityIthacaUSA

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