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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
Published electronically: August 18, 2009
MathSciNet review: 2534594
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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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Additional Information

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

Emanuel Stoica
Affiliation: Department of Mathematics, Room 2-089, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

Stephen Griffeth
Affiliation: School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, Minnesota 55455

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

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