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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Unitary representations of rational Cherednik algebras
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by Pavel Etingof and Emanuel Stoica; with an appendix by Stephen Griffeth PDF
Represent. Theory 13 (2009), 349-370 Request permission


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
  • MR Author ID: 289118
  • Email:
  • Emanuel Stoica
  • Affiliation: Department of Mathematics, Room 2-089, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
  • Email:
  • Stephen Griffeth
  • Affiliation: School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, Minnesota 55455
  • Email:
  • 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:
  • MathSciNet review: 2534594