Number Theory Seminar: Sharon Frechette

We construct Weyl group multiple Dirichlet series associated to root systems of type C, through a combinatorial recipe involving Gelfand-Tsetlin patterns. These Dirichlet series are associated with an n-fold metaplectic cover of SO(2r+1) and we prove functional equations for them when n=1, via the Casselman-Shalika formula. We also prove that our description matches the so called "stable case," as described for general root systems by Brubaker, Bump and Friedberg. This is joing work with Jennifer Beineke and Ben Brubaker.