Weyl group multiple dirichlet series of type C

Jennifer Beineke, Benjamin Brubaker, Sharon Frechette

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We develop the theory of Weyl group multiple Dirichlet series for root systems of type C. For a root system of rank r and a positive integer n, these are Dirichlet series in r complex variables with analytic continuation and functional equations isomorphic to the associated Weyl group. They conjecturally arise as Whittaker coefficients of Eisenstein series on a metaplectic group with cover degree n. For type C and n odd, we construct an infinite family of Dirichlet series and prove they satisfy the above analytic properties in many cases. The coefficients are exponential sums built from Gelfand-Tsetlin bases of certain highest weight representations. Previous attempts to define such series by Brubaker, Bump, and Friedberg required n sufficiently large, so that coefficients were described by Weyl group orbits. We demonstrate that these two radically different descriptions match when both are defined. Moreover, for n = 1, we prove our series are Whittaker coefficients of Eisenstein series on SO(2r+1).

Original languageEnglish (US)
Pages (from-to)11-46
Number of pages36
JournalPacific Journal of Mathematics
Volume254
Issue number1
DOIs
StatePublished - 2011

Keywords

  • Eisenstein series
  • Gelfand-Tsetlin pattern
  • Metaplectic group
  • Weyl group multiple Dirichlet series

Fingerprint Dive into the research topics of 'Weyl group multiple dirichlet series of type C'. Together they form a unique fingerprint.

Cite this