Unitary representations of rational Cherednik algebras

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dc.creatorEtingof, Pavel
dc.creatorStoica, Emanuel
dc.creatorGriffeth, Stephen
dc.date2009-01-29
dc.date2009-03-20
dc.date.accessioned2026-07-07T12:54:12Z
dc.date.available2026-07-07T12:54:12Z
dc.descriptionWe 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).
dc.description31 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
dc.identifierhttps://arxiv.org/abs/0901.4595
dc.identifierhttp://arxiv.org/abs/0901.4595
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223846
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.titleUnitary representations of rational Cherednik algebras
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