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- W2153830331 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 [GS1]; the other involving quantum hamiltonian reduction of an algebra of differential operators [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 $${fancyscript {D}}$$ -modules with the shift functor for the Cherednik algebra. That enables us to give a direct and relatively short proof of the key result [GS1, Theorem 1.4] without recourse to Haiman’s deep results on the n! theorem [Ha1]. We also show that the characteristic cycles defined independently in these two approaches are equal, thereby confirming a conjecture from [GG]." @default.
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- W2153830331 date "2009-02-27" @default.
- W2153830331 modified "2023-09-26" @default.
- W2153830331 title "Differential operators and Cherednik algebras" @default.
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- W2153830331 doi "https://doi.org/10.1007/s00029-009-0515-z" @default.
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