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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

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

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).

References
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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