Realizing the local Weil representation over a number field

Gerald Cliff and David McNeilly

Vol. 255 (2012), No. 1, 55–77

DOI: 10.2140/pjm.2012.255.55

Abstract

Let F be a non-Archimedean local field whose residue field has order q and characteristic p≠2. We show that the Weil representations of the symplectic group Sp(2n,F) can be realized over the field

Furthermore, the field E₀ is shown to be optimal if q ≡ 1 mod 4.

Keywords

Weil representation, local fields

Mathematical Subject Classification 2000

Primary: 11F70, 22E50

Milestones

Received: 9 April 2009

Revised: 18 August 2011

Accepted: 24 October 2011

Published: 14 March 2012