Differential operators and Cherednik algebras

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dc.creatorGinzburg, V.
dc.creatorGordon, I.
dc.creatorStafford, J. T.
dc.date2008-03-23
dc.date.accessioned2026-07-07T09:28:15Z
dc.date.available2026-07-07T09:28:15Z
dc.descriptionWe 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, used in [GS]; the other involving quantum hamiltonian reduction of an algebra of differential operators, used in [GG]. In the present 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, [GS, Theorem 1.4] without recourse to Haiman's deep results on the n! theorem. We also show that the characteristic cycles defined independently in these two approaches are equal, thereby confirming a conjecture from [GG].
dc.description37 pp
dc.identifierhttps://arxiv.org/abs/0803.3349
dc.identifierhttp://arxiv.org/abs/0803.3349
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157388
dc.subjectQuantum Algebra
dc.subjectAlgebraic Geometry
dc.subjectRings and Algebras
dc.titleDifferential operators and Cherednik algebras
dc.typetext

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