Projects per year
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.
Original language  English 

Pages (fromto)  23272386 
Number of pages  60 
Journal  Algebra and Number Theory 
Volume  12 
Issue number  10 
DOIs  
Publication status  Published  1 Feb 2019 
Keywords
 Endoparameter
 Jordan block
 Local langlands correspondence
 Padic group
 Symplectic group
 Types and covers
Profiles

Shaun Stevens
 School of Mathematics  Professor of Mathematics
 Algebra and Combinatorics  Member
Person: Research Group Member, Academic, Teaching & Research
Projects
 2 Finished

Explicit Correspondences in Number Theory.
Engineering and Physical Sciences Research Council
31/03/10 → 30/03/15
Project: Fellowship

Explicit and Imodular theta correspondence
Engineering and Physical Sciences Research Council
15/07/08 → 14/01/12
Project: Research