Recollement of Deformed Preprojective Algebras and the Calogero-Moser Correspondence

Simple item page
dc.creatorBerest, Yuri
dc.creatorChalykh, Oleg
dc.creatorEshmatov, Farkhod
dc.date2007-06-20
dc.date.accessioned2026-07-07T08:11:22Z
dc.date.available2026-07-07T08:11:22Z
dc.descriptionThe 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(\C)$; $ (b) $ simple modules over deformed preprojective algebras $ Π_λ(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 $\A$-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/Γ$, where $ Γ$ is a finite cyclic subgroup of $ \SL(2, \C) $.
dc.description16 pp., LaTex, to appear in Moscow Math. J.(2007)
dc.identifierhttps://arxiv.org/abs/0706.3006
dc.identifierhttp://arxiv.org/abs/0706.3006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132100
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.titleRecollement of Deformed Preprojective Algebras and the Calogero-Moser Correspondence
dc.typetext

Files

Collections

arXiv