2008/03/23 by Ginzburg, V., Gordon, I., Stafford, J. T.
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.0803.3349
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].