# Recollement of Deformed Preprojective Algebras and the Calogero-Moser Correspondence

Berest, Y, Chalykh, O and Eshmatov, F (2008) Recollement of Deformed Preprojective Algebras and the Calogero-Moser Correspondence. Moscow Mathematical Journal, 8 (1). ISSN 1609-4514

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## Abstract

The aim of this paper is to clarify the relation between the following objects: (a) rank 1 projective modules (ideals) over the first Weyl algebra A_1; (b) simple modules over deformed preprojective algebras $\Pi_{\lambda}(Q)$ introduced by Crawley-Boevey and Holland; and (c) simple modules over the rational Cherednik algebras $H_{0,c}(S_n)$ associated to symmetric groups. The isomorphism classes of each type of these objects can be parametrized geometrically by the same space (namely, the Calogero-Moser algebraic varieties); however, no natural functors between the corresponding module categories seem to be known. We construct such functors by translating our earlier results on A-infinity modules over A_1 to a more familiar setting of representation theory. In the last section we extend our construction to the case of Kleinian singularities $C^2/\Gamma$, where $\Gamma$ is a finite cyclic subgroup of $SL(2,C)$.

Item Type: Article © 2008, Independent University of Moscow. This is an author produced version of a paper published in Moscow Mathematical Journal. Uploaded with permission from the publisher. Weyl algebra, deformed preprojective algebra, Cherednik algebra The University of Leeds The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) Symplectic Publications 02 Jul 2012 09:33 09 Jun 2014 17:43 Published Independent University of Moscow http://eprints.whiterose.ac.uk/id/eprint/74390