Unitary representations of rational Cherednik algebras

Etingof, Pavel; Stoica, Emanuel

doi:10.1090/S1088-4165-09-00356-2

Unitary representations of rational Cherednik algebras
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by Pavel Etingof and Emanuel Stoica; with an appendix by Stephen Griffeth

Represent. Theory 13 (2009), 349-370

DOI: https://doi.org/10.1090/S1088-4165-09-00356-2

Published electronically: August 18, 2009

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Abstract:

We study unitarity of lowest weight irreducible representations of rational Cherednik algebras. We prove several general results, and use them to determine which lowest weight representations are unitary in a number of cases.

In particular, in type A, we give a full description of the unitarity locus (justified in Subsection 5.1 and the appendix written by S. Griffeth), and resolve a question by Cherednik on the unitarity of the irreducible subrepresentation of the polynomial representation. Also, as a by-product, we establish Kasatani’s conjecture in full generality (the previous proof by Enomoto assumes that the parameter $c$ is not a half-integer).

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