Splittings of the metaplectic covers of some reductive dual pairs

Shu-Yen Pan

Vol. 199 (2001), No. 1, 163–226

DOI: 10.2140/pjm.2001.199.163

Abstract

In this paper, we construct a splitting of the metaplectic cover of the reductive dual pairs of orthogonal and symplectic groups or the reductive dual pairs of unitary groups over a nonarchimedean local field with respect to a generalized lattice model of the Weil representation. We also prove a result concerning the splitting that we construct and the theta dichotomy for unitary group. The splitting plays a very crucial role in the study of theta correspondence for p-adic and finite reductive dual pairs.

Milestones

Received: 29 April 1999

Revised: 21 March 2000

Published: 1 May 2001