Unitary representations of rational Cherednik algebras
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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 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).
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
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