Seminar

I will explain how the category of equivariant D-modules on a reductive Lie algebra has a block decomposition, where the blocks are indexed by conjugacy classes of cuspidal local systems on Levi subalgebras.  Each block admits an explicit description as modules for a specialization of a rational Cherednik algebra. This theorem generalizes (further) Lusztig's generalized Springer correspondence, and in particular, leads to a new a new and intuitive proof of some of Lusztig's results. Time permitting, I will discuss some work in progress towards seeing more general Cherednik algebras.