Z. Yun

Springer representations and Hitchin fibration

Classical Springer representation is the action of the Weyl group on the cohomology of certain subvarieties of the flag variety. I will construct a global analogue of this action, namely, an action of the graded double affine Hecke algebra on the cohomology of parabolic Hitchin fibers. Examples in GL(2) will be described in details, where we can already see new phenomena compared to the classical Springer theory. Time permitting, I will explain the relation between this construction and geometric Langlands duality.