Differential operators and Cherednik algebras
نویسندگان
چکیده
منابع مشابه
Differential operators and Cherednik algebras
We establish a link between two geometric approaches to the representation theory of rational Cherednik algebras of type A: one based on a noncommutative Proj construction [GS1]; the other involving quantum hamiltonian reduction of an algebra of differential operators [GG]. In this paper, we combine these two points of view by showing that the process of hamiltonian reduction intertwines a natu...
متن کاملA Remark on Rational Cherednik Algebras and Differential Operators on the Cyclic Quiver
We show that the spherical subalgebra Uk,c of the rational Cherednik algebra associated to Sn o C`, the wreath product of the symmetric group and the cyclic group of order `, is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver of size `. This confirms a version of [EG, Conjecture 11.22] in the case of cyclic groups. The ...
متن کاملA Remark on Rational Cherednik Algebras and Differential Operators on the Cyclic Quiver
We show that the spherical subalgebra Uk,c of the rational Cherednik algebra associated to Sn ≀ Cl, the wreath product of the symmetric group and the cyclic group of order l, is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver of size l. This confirms a version of [EG, Conjecture 11.22] in the case of cyclic groups. The ...
متن کاملCherednik algebras and Yangians
We construct a functor from the category of modules over the trigonometric (resp. rational) Cherednik algebra of type gll to the category of integrable modules of level l over a Yangian for the loop algebra sln (resp. over a subalgebra of this Yangian called the Yangian deformed double loop algebra) and we establish that it is an equivalence of categories if l + 2 < n.
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: Selecta Mathematica
سال: 2009
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-009-0515-z