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 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]. © 2009 Birkhäuser Verlag Basel/Switzerland.
Original language | English |
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Pages (from-to) | 629-666 |
Number of pages | 37 |
Journal | Selecta Mathematica |
Volume | 14 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - May 2009 |
Keywords
- Characteristic varieties
- Cherednik algebra
- Hilbert scheme