Weil representation and transfer factor

Thomas, Teruji

doi:10.2140/ant.2013.7.1535

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Weil representation and transfer factor

Teruji Thomas

Vol. 7 (2013), No. 7, 1535–1570

DOI: 10.2140/ant.2013.7.1535

Abstract

This paper concerns the Weil representation of the semidirect product of the metaplectic and Heisenberg groups. First we present a canonical construction of the metaplectic group as a central extension of the symplectic group by a subquotient of the Witt group. This leads to simple formulas for the character, for the inverse Weyl transform, and for the transfer factor appearing in J. Adams’s work on character lifting. Along the way, we give formulas for outer automorphisms of the metaplectic group induced by symplectic similitudes. The approach works uniformly for finite and local fields.

Keywords

metaplectic group, Weil representation, Weyl transform, transfer factor, Cayley transform, Maslov index

Mathematical Subject Classification 2010

Primary: 11F27

Secondary: 20C15

Milestones

Received: 14 August 2011

Revised: 5 June 2012

Accepted: 5 July 2012

Published: 12 October 2013

Authors

Teruji Thomas
School of Mathematics University of Edinburgh JCMB, The King’s Buildings Mayfield Road Edinburgh EH9 3JZ United Kingdom

Vol. 7, No. 7, 2013