Solomon Friedberg, Boston College

Fri., June 5 at 1 pm in MS 6221

Metaplectic Eisenstein series, twisted Euler products, and crystal graphs

Abstract: The Whittaker coefficients of classical Eisenstein series are Euler products and may be expressed in terms of Langlands L-functions. By contrast, the Whittaker coefficients of metaplectic Eisenstein series are typically not Eulerian. In this talk, I will describe joint work with Ben Brubaker (MIT) and Dan Bump (Stanford) which shows that for Borel Eisenstein series on the n-fold cover of GL(r), they nonetheless have a rich number-theoretic structure. Indeed, they are twisted Euler products (a notion I will define). Moreover, their p-parts can be described by attaching products of Gauss sums to the vertices of certain crystal graphs that arise in the study of representations of quantum groups, in a way that makes use of the graph structure, which in turn reflects aspects of the theory of quantum groups. (I will not assume knowledge of quantum groups.)