Noncommutative Dunkl operators and braided 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...
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In this paper we prove the existence of the Dunkl weight function Kc,λ for any irreducible representation λ of any finite Coxeter group W , generalizing previous results of Dunkl. In particular, Kc,λ is a family of tempered distributions on the real reflection representation of W taking values in EndC(λ), with holomorphic dependence on the complex multi-parameter c. When the parameter c is real...
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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.
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2009
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-009-0525-x