Algebra and Geometry Seminar
The rational double affine Hecke algebra (DAHA) of a Weyl group W is an analogue of the universal enveloping algebra of a semisimple Lie algebra. We define a remarkable module over the rational DAHA that depends on its so-called central charge. At successively more special values of the central charge, we can determine successively stronger properties of the module. We relate it with Deligne-Lusztig characters, with point-counting on iterated bundles over flag varieties, and with affine Springer fibers. Time permitting, we will explain a conjecture involving the last two, expected to be a P = W phenomenon in the sense of nonabelian Hodge theory.