Unitary representations of rational Cherednik algebras

Details Unitary representations of rational Cherednik algebras Unitary representations of rational Cherednik algebras

2009-01-29

arxiv.org/abs/0901.4595v3

Mathematics

Representation Theory

31 pages, latex; the present version contains an appendix by Stephen Griffeth, which allowed to make Conjecture 5.5 from the p

Scientific paper

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).

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