Weyl Group Multiple Dirichlet Series for Type C
by
Sharon Frechette
College of the Holy Cross
Coauthors: Jennifer Beineke (Western New England College) Ben Brubaker (Massachusetts Institute of Technology)

Given a reduced root system F of rank r, we may attach a multiple Dirichlet series in r complex variables, whose group of functional equations is isomorphic to the Weyl group of F. These multiple Dirichlet series contain interesting arithmetic information. A primary goal is to use them to provide combinatorial definitions of Fourier-Whittaker coefficients of Eisenstein series on certain arithmetic covers of metaplectic groups. We discuss a construction of a multiple Dirichlet series associated to the root systems of type C_r, which are conjecturally associated to minimal parabolic Eisenstein series on n-fold metaplectic covers of SO(2r+1), with r ≥ 1 and n ≥ 1 odd.

Date received: May 4, 2008