Local symmetric square $L$-factors of representations of general linear groups

Shunsuke Yamana

Vol. 286 (2017), No. 1, 215–256

DOI: 10.2140/pjm.2017.286.215

Abstract

This paper develops a theory of local symmetric square $L$-factors of representations of general linear groups. We will prove a certain characterization of a pole of symmetric square $L$-factors of square-integrable representations, the uniqueness of certain trilinear forms and the nonexistence of Whittaker models of higher exceptional representations.

Keywords

symmetric square $L$-factors, exceptional representations, distinguished representations

Mathematical Subject Classification 2010

Primary: 11F66

Secondary: 11F70

Milestones

Received: 30 April 2015

Revised: 3 September 2015

Accepted: 14 June 2016

Published: 9 December 2016