Unitary Representations of Rational Cherednik Algebras
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Etingof Representation Theory p.349_unlocked.pdf
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Author(s)
Etingof, Pavel I.
Stoica, Emanuel I.
Griffeth, Stephen
Date Issued
August 2009
Journal
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
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).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1090/S1088-4165-09-00356-2
