Abstract

This talk will report on joint work with Victor Ginzburg and Iain Gordon.

Type A Cheredink algebras H_c, which are particular deformations of the twisted group ring of the n-th Weyl algebra by the symmetric group S_n, form an intriguing class of algebras with many interactions with other areas of mathematics. In earlier work with Iain Gordon we used ideas from noncommutative geometry to prove a sort of Beilinson-Bernstein equivalence of categories, thereby showing that H_c (or more formally its spherical subalgebra U_c) is a noncommutative deformation of the Hilbert scheme Hilb(n) of n points in the plane.

There is however a second way of relating U_c to Hilbert schemes, which uses the quantum Hamiltonian reduction of Gan and Ginzburg. In the first part of the talk we will show that these two methods are actually equivalent. In the second part of the talk we will use this to prove that the characteristic varieties of irreducible U_c-modules are equidimensional subshemes of Hilb(n), thereby answering a question from the original work with Gordon.