Unitary representations of rational Cherednik algebras

Authors:
Pavel Etingof and Emanuel Stoica; with an appendix by Stephen Griffeth

Journal:
Represent. Theory **13** (2009), 349-370

MSC (2000):
Primary 16S99

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

Published electronically:
August 18, 2009

MathSciNet review:
2534594

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 is not a half-integer).

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Additional Information

**Pavel Etingof**

Affiliation:
Department of Mathematics, Room 2-176, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

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

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

Received by editor(s):
May 5, 2009

Received by editor(s) in revised form:
June 12, 2009

Published electronically:
August 18, 2009

Article copyright:
© Copyright 2009
American Mathematical Society