Unitary representations of rational Cherednik algebras
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 complete description of the unitarity locus (justified in Section 5 and appendix by Stephen 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).
Keywords
Cite
@article{arxiv.0901.4595,
title = {Unitary representations of rational Cherednik algebras},
author = {Pavel Etingof and Emanuel Stoica and Stephen Griffeth},
journal= {arXiv preprint arXiv:0901.4595},
year = {2009}
}
Comments
31 pages, latex; the present version contains an appendix by Stephen Griffeth, which allowed to make Conjecture 5.5 from the previous version into Theorem 5.5