The Weil representation and Gauss sums

Antonia Wilson Bluher

Vol. 173 (1996), No. 2, 357–373

DOI: 10.2140/pjm.1996.173.357

Abstract

We use the Weil representation to evaluate certain Gauss sums over a local field, up to ±1. Also we construct a cocycle on Sp(2m, ℝ) with a simple formula on the maximal compact torus and we show how to lift homomorphisms j : Sp(2n, ℝ) → Sp(2m, ℝ) to the double covers of these groups.

Mathematical Subject Classification 2000

Primary: 11L05

Secondary: 11F27

Milestones

Received: 14 September 1993

Revised: 9 May 1994

Published: 1 April 1996