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Jordan blocks of
cuspidal representations of symplectic groups
Corinne Blondel, Guy Henniart and Shaun Stevens |
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Vol. 12 (2018), No. 10, 2327–2386
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Abstract |
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Let be a symplectic group over a nonarchimedean local field of characteristic zero and odd residual characteristic. Given an irreducible cuspidal representation of , 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 , giving a bijection between the set of endoparameters for and the set of restrictions to wild inertia of discrete Langlands parameters for , 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 , 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. |
Keywords
local Langlands correspondence, symplectic group, $p$-adic
group, Jordan block, endoparameter, types and covers
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Mathematical Subject Classification 2010
Primary: 22E50
Secondary: 11F70
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Milestones
Received: 30 May 2017
Revised: 2 June 2018
Accepted: 20 July 2018
Published: 1 February 2019
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Authors |
| Corinne Blondel | |
| CNRS-IMJ-PRG Université Paris Diderot Paris France |
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| Guy Henniart | |
| Université de Paris-Sud Laboratoire de Mathématiques d’Orsay Orsay France |
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| Shaun Stevens | |
| School of Mathematics University of East Anglia Norwich United Kingdom |
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