Theta lifts of strongly positive discrete series: [2pt] the case of (Sp(n),O(V ))

Ivan Matić

Vol. 259 (2012), No. 2, 445–471

DOI: 10.2140/pjm.2012.259.445

Abstract

Let F denote a nonarchimedean local field of characteristic zero with odd residual characteristic. Using the results of Gan and Savin, in this paper we determine the first occurrence indices and theta lifts of strongly positive discrete series representations of metaplectic groups over F in terms of our recent classification of this class of representations. Also, we determine the first occurrence indices of some strongly positive representations of odd orthogonal groups.

Keywords

theta correspondence, metaplectic groups, strongly positive representations

Mathematical Subject Classification 2010

Primary: 22E35, 22E50

Secondary: 11F27

Milestones

Received: 8 March 2011

Revised: 14 July 2012

Accepted: 16 July 2012

Published: 3 October 2012