Dierential operators and Cherednik algebras

Ginzburg, V and Gordon, I G and Stafford, J T (2009) Dierential operators and Cherednik algebras. Selecta Math., 14. pp. 629-666. ISSN 1022-1824

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Abstract

We establish a link betweentwo geometric approaches to the representation theory of rationalCherednik algebras of type A: one based on anoncommutative Proj construction \cite{GS}; the other involving quantum hamiltonian reduction of an algebra of differential operators \cite{GG}. In this paper, we combine these two points of view by showing that the process of hamiltonian reduction intertwines a naturally defined geometric twist functor on D-modules with the shift functor for the Cherednik algebra.That enables us to give a direct and relatively short proof of the key result \cite[Theorem~1.4]{GS} without recourse to Haiman's deep results on the n! theorem \cite{Ha1}. We also show that the characteristic cycles defined independently in these two approaches are equal, thereby confirming a conjecture from \cite{GG}.

Item Type: Article
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry
MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras
Depositing User: Professor J T Stafford
Date Deposited: 15 May 2013
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1976

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