Weyl group multiple Dirichlet series II: The stable case |
| |
Authors: | Ben Brubaker Daniel Bump Solomon Friedberg |
| |
Affiliation: | (1) Department of Mathematics, Stanford University, Stanford, CA 94305-2125, USA;(2) Department of Mathematics, Boston College, Chestnut Hill, MA 02467-3806, USA |
| |
Abstract: | To each reduced root system Φ of rank r, and each sufficiently large integer n, we define a family of multiple Dirichlet series in r complex variables, whose group of functional equations is isomorphic to the Weyl group of Φ. The coefficients in these Dirichlet series exhibit a multiplicativity that reduces the specification of the coefficients to those that are powers of a single prime p. For each p, the number of nonzero such coefficients is equal to the order of the Weyl group, and each nonzero coefficient is a product of n-th order Gauss sums. The root system plays a basic role in the combinatorics underlying the proof of the functional equations. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|