## Student Number Theory Seminar 2019-20

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2/17/20: Claire Frechette -- *New Yang-Baxter Equations for Metaplectic Ice*

**Abstract:** As part of my oral exam paper, I worked on extending existing connections between quantum groups and spherical Whittaker models on metaplectic covering groups of GL(r,F) over local fields. Brubaker, Buciumas, and Bump showed that for a certain metaplectic n-fold cover of GL(r,F) a set of Yang-Baxter equations govern the behavior of the Whittaker functions and that these equations arise from a Drinfeld twist of a quantum affine Lie superalgebra. I will talk about extend their results to all metaplectic covers of GL(r,F), showing that the same Yang-Baxter equations underlie the scattering matrix for the Whittaker functions in the general case, and that these equations arise from Drinfeld twists of quantum groups. (I will also define what most of these words mean.) If you've been in Ben's class this semester, this is one motivating case for why you should care about that class, and a sneak preview of some stuff that's to come!