## 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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## Bibliographic Information

**Pavel Etingof**- Affiliation: Department of Mathematics, Room 2-176, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
- MR Author ID: 289118
- Email: etingof@math.mit.edu
**Emanuel Stoica**- Affiliation: Department of Mathematics, Room 2-089, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
- Email: immanuel@math.mit.edu
**Stephen Griffeth**- Affiliation: School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, Minnesota 55455
- Email: griffeth@math.umn.edu
- Received by editor(s): May 5, 2009
- Received by editor(s) in revised form: June 12, 2009
- Published electronically: August 18, 2009
- © Copyright 2009 American Mathematical Society
- Journal: Represent. Theory
**13**(2009), 349-370 - MSC (2000): Primary 16S99
- DOI: https://doi.org/10.1090/S1088-4165-09-00356-2
- MathSciNet review: 2534594