Unitary representations of cyclotomic rational Cherednik algebras
نویسندگان
چکیده
منابع مشابه
Unitary Representations of Rational Cherednik Algebras
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 b...
متن کاملCuspidal Representations of Rational Cherednik Algebras
We study those finite dimensional quotients of the rational Cherednik algebra at t = 0 that are supported at a point of the centre. It is shown that each such quotient is Morita equivalent to a certain “cuspidal” quotient of a rational Cherednik algebra associated to a parabolic subgroup of W .
متن کاملOn Category O for Cyclotomic Rational Cherednik Algebras
We study equivalences for category Op of the rational Cherednik algebras Hp of type G`(n) = (μ`) n o Sn: a highest weight equivalence between Op and Oσ(p) for σ ∈ S` and an action of S` on a non-empty Zariski open set of parameters p; a derived equivalence between Op and Op′ whenever p and p′ have integral difference; a highest weight equivalence between Op and a parabolic category O for the ge...
متن کاملFe b 20 09 Unitary representations of rational Cherednik
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 b...
متن کاملRational Cherednik algebras
We survey a number of results about rational Cherednik algebra representation theory and its connection to symplectic singularities and their resolutions. Mathematics Subject Classification (2000). Primary 16G, 17B; Secondary 20C, 53D.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2018
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2018.07.011