Reducibility points and characteristic p local fields I Simple supercuspidal representations of symplectic groups.

Blondel, Corinne, Henniart, Guy and Stevens, Shaun (2026) Reducibility points and characteristic p local fields I Simple supercuspidal representations of symplectic groups. Bulletin of the London Mathematical Society. ISSN 0024-6093 (In Press)

Preview

PDF (BHS3-charpI-final) - Accepted Version Available under License Creative Commons Attribution. Download (312kB) | Preview

Abstract

Let F be a non-Archimedean local field with odd characteristic p. Let N be a positive integer and G=Sp2N(F). By work of Lomelí on γ-factors of pairs and converse theorems, a generic supercuspidal representation π of G has a transfer to a smooth irreducible representation Ππ of GL2N+1(F). In turn the Weil–Deligne representation Σπ associated to Ππ by the Langlands correspondence determines a Langlands parameter ϕπ for π. This process produces a Langlands correspondence for generic cuspidal representations of G. In this paper we take π to be simple in the sense of Gross and Reeder, and from the explicit construction of π we describe Ππ explicitly. The method we use is the same as in a previous paper, where we treated the case where F is a p-adic field. It relies on a criterion due to Mœglin on the reducibility of representations parabolically induced from GLM(F)xG for varying positive integers M. We extend this criterion to the case when F has any positive characteristic. The main new feature consists in relating reducibility to γ-factors for pairs.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	LivePure Connector
Date Deposited:	01 May 2026 10:49
Last Modified:	01 May 2026 10:49
URI:	https://ueaeprints.uea.ac.uk/id/eprint/102875
DOI:	issn:0024-6093

Downloads

Actions (login required)

View Item