Derived equivalences for rational Cherednik algebras
نویسندگان
چکیده
منابع مشابه
Rational 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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These are notes for a talk in the MIT-Northeastern Spring 2015 Graduate Representation Theory Seminar. The main source is [BR14].
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We construct a microlocalization of the rational Cherednik algebras H of type Sn. This is achieved by a quantization of the Hilbert scheme Hilb C2 of n points in C2. We then prove the equivalence of the category of H -modules and that of modules over its microlocalization under certain conditions on the parameter.
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We construct and study some finite dimensional modules for rational Cherednik algebras for the groups G(r, p, n) by using intertwining operators and a commutative family of operators introduced by Dunkl and Opdam. The coinvariant ring and an analog of the ring constructed by Gordon in the course of proving Haiman’s conjectures on diagonal coinvariants are special cases. We study a certain hyper...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2017
ISSN: 0012-7094
DOI: 10.1215/00127094-3674223