# Seminars & Colloquia Calendar

## Metaplectic representations of Hecke algebras and a new family of polynomials

#### Vidya Venkateswaran, Center for Communications Research at Princeton

Location: ** Hill 705**

Date & time: Friday, 06 December 2019 at 10:30AM - 11:30AM

**Abstract:**In this talk, we will discuss some recent joint work with Siddhartha Sahi and Jasper Stokman. We introduce a new \metaplectic" action of the double ane Hecke algebra on polynomials.- Next, we show how one can obtain the hinta-Gunnells Weyl group action (a key ingredient in their construction of Weyl group multiple Dirichlet series) via localization. Finally, we show that there exist families of metaplectic polynomials indexed by the weight lattice, and depending on additional parameters, which are eigenfunctions of metaplectic variants of Cherednik's Y -operators. These polynomials satisfy various nice properties, and special cases connect with well-studied objects. In particular, they reduce to nonsymmetric Macdonald polynomials at n = 1, and metaplectic Iwahori-Whittaker functions can be obtained by taking a limit in the q-parameter.

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