Monday, November 11, 2019
4:00 PM -
5:00 PM
Linde Hall 387
Algebra and Geometry Seminar
Manifestations of a Rational DAHA Module in Moduli of Flags
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.
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For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].