Weyl Group Multiple Dirichlet Series for Symmetrizable Kac-Moody Root Systems

TL;DR

This paper extends the construction of Weyl group multiple Dirichlet series from finite root systems to those associated with symmetrizable Kac-Moody algebras, establishing their key properties.

Contribution

It generalizes previous finite root system results to symmetrizable Kac-Moody root systems, including functional equations and meromorphic continuation.

Findings

Constructed Weyl group multiple Dirichlet series for Kac-Moody root systems

Proved functional equations for these series

Established meromorphic continuation

Abstract

Weyl group multiple Dirichlet series, introduced by Brubaker, Bump, Chinta, Friedberg and Hoffstein, are expected to be Whittaker coefficients of Eisenstein series on metaplectic groups. Chinta and Gunnells constructed these multiple Dirichlet series for all the finite root systems using the method of averaging a Weyl group action on the field of rational functions. In this paper, we generalize Chinta and Gunnells' work and construct Weyl group multiple Dirichlet series for the root systems associated with symmetrizable Kac-Moody algebras, and establish their functional equations and meromorphic continuation.