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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 [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 Dmodules 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].
Original language  English 

Pages (fromto)  629666 
Number of pages  38 
Journal  Selecta Mathematica (New Series) 
Volume  14 
Issue number  34 
DOIs  
Publication status  Published  May 2009 
Keywords
 Cherednik algebra
 Hilbert scheme
 characteristic varieties
 FINITEDIMENSIONAL REPRESENTATIONS
 HILBERT SCHEMES
Projects
 1 Finished

RIGID STRUCTURE IN NONCOMMUTATIVE, GEOMETRIC & COMBINATORIAL PROBLEMS
1/09/08 → 30/06/14
Project: Research