Algebra & Number Theory
- Algebra Number Theory
- Volume 12, Number 10 (2018), 2327-2386.
Jordan blocks of cuspidal representations of symplectic groups
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.
Algebra Number Theory, Volume 12, Number 10 (2018), 2327-2386.
Received: 30 May 2017
Revised: 2 June 2018
Accepted: 20 July 2018
First available in Project Euclid: 14 February 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Blondel, Corinne; Henniart, Guy; Stevens, Shaun. Jordan blocks of cuspidal representations of symplectic groups. Algebra Number Theory 12 (2018), no. 10, 2327--2386. doi:10.2140/ant.2018.12.2327. https://projecteuclid.org/euclid.ant/1550113225