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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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Authors and Affiliations

  1. Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, SAR, China

    JING-SONG HUANG

  2. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    KAYUE DANIEL WONG

Authors
  1. JING-SONG HUANG
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  2. KAYUE DANIEL WONG
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Correspondence to JING-SONG HUANG.

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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

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