Jordan blocks of cuspidal representations of symplectic groups

Blondel, Corinne, Henniart, Guy and Stevens, Shaun (2019) Jordan blocks of cuspidal representations of symplectic groups. Algebra and Number Theory, 12 (10). pp. 2327-2386. ISSN 1937-0652

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Abstract

Let G be a symplectic group over a nonarchimedean local field of characteristic zero and odd residual characteristic. Given an irreducible cuspidal representation of G, we determine its Langlands parameter (equivalently, its Jordan blocks in the language of Mœglin) in terms of the local data from which the representation is explicitly constructed, up to a possible unramified twist in each block of the parameter. We deduce a ramification theorem for G, giving a bijection between the set of endoparameters for G and the set of restrictions to wild inertia of discrete Langlands parameters for G, compatible with the local Langlands correspondence. The main tool consists in analyzing the Hecke algebra of a good cover, in the sense of Bushnell–Kutzko, for parabolic induction from a cuspidal representation of G × GL n , seen as a maximal Levi subgroup of a bigger symplectic group, in order to determine reducibility points; a criterion of Mœglin then relates this to Langlands parameters.

Item Type:	Article
Uncontrolled Keywords:	endoparameter,jordan block,local langlands correspondence,p-adic group,symplectic group,types and covers,algebra and number theory ,/dk/atira/pure/subjectarea/asjc/2600/2602
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	23 Jul 2018 15:30
Last Modified:	13 May 2023 00:36
URI:	https://ueaeprints.uea.ac.uk/id/eprint/67812
DOI:	10.2140/ant.2018.12.2327

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