Unitary Representations of Rational Cherednik Algebras
Author(s)
Etingof, Pavel I.; Stoica, Emanuel I.; Griffeth, Stephen
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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).
Date issued
2009-08Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Representation Theory
Publisher
American Mathematical Society
Citation
Etingof, Pavel and Emanuel Stoica. "Unitary Representations of Rational Cherednik Algebras." Representation Theory. 13 (2009): 349–370 © 2009 American Mathematical Society
Version: Final published version
ISSN
1088-4165