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arXiv · 0803.3349

Differential operators and Cherednik algebras

V. Ginzburg·I. Gordon·J. T. Stafford
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Abstract

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, 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].

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BibTeXRIS

V. Ginzburg, I. Gordon, J. T. Stafford. 2008-03-23. Differential operators and Cherednik algebras. https://arxiv.org/abs/0803.3349

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