Symplectic supercuspidal representations of GL(2n) over p-adic fields

Dihua Jiang, Chufeng Nien and Yujun Qin

Vol. 245 (2010), No. 2, 273–313

DOI: 10.2140/pjm.2010.245.273

Abstract

This is part two of the authors’ work on supercuspidal representations of GL(2n) over p-adic fields. We consider the complete relations among the local theta correspondence, local Langlands transfer, and the local descent attached to a given irreducible symplectic supercuspidal representation of p-adic GL_2n. This is the natural extension of the work of Ginzburg, Rallis and Soudry and of Jiang and Soudry on the local descents and the local Langlands transfers. The approach undertaken in this paper is purely local. A mixed approach with both local and global methods, which works for more general classical groups, has been considered by Jiang and Soudry.

Keywords

symplectic representation, Shalika models, local Langlands transfer, local descent, supercuspidal, representations of p-adic groups

Mathematical Subject Classification 2000

Primary: 11F70, 22E50

Secondary: 11F85, 22E55

Milestones

Received: 7 January 2009

Accepted: 8 October 2009

Published: 1 April 2010