Projects per year
Abstract
Let be an orthogonal, symplectic or unitary group over a nonarchimedean local field of odd residual characteristic. This paper concerns the study of the “wild part” of an irreducible smooth representation of , encoded in its “semisimple character”. We prove two fundamental results concerning them, which are crucial steps toward a complete classification of the cuspidal representations of . First we introduce a geometric combinatorial condition under which we prove an “intertwining implies conjugacy” theorem for semisimple characters, both in and in the ambient general linear group. Second, we prove a Skolem–Noether theorem for the action of on its Lie algebra; more precisely, two semisimple elements of the Lie algebra of which have the same characteristic polynomial must be conjugate under an element of if there are corresponding semisimple strata which are intertwined by an element of .
Original language  English 

Pages (fromto)  137205 
Number of pages  69 
Journal  Nagoya Mathematical Journal 
Volume  238 
Early online date  16 Jul 2018 
DOIs  
Publication status  Published  Jun 2020 
Profiles

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

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