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Algebra and Geometry Seminar

Monday, November 11, 2019
4:00pm to 5:00pm
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Linde Hall 387
Manifestations of a Rational DAHA Module in Moduli of Flags
Minh-Tam Trinh, Department of Mathematics, University of Chicago,

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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