Projects per year
Abstract
The Local Converse Problem is to determine how the family of twisted local gamma factors characterizes the isomorphism class of an irreducible admissible generic representation of GL(n,F), with F a nonarchimedean local field, where the twists run through all irreducible supercuspidal representations of GL(r,F) and r runs through positive integers. The Jacquet conjecture asserts that it is enough to take r = 1,2,...,[n/2]. Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture, we formulate a general approach to prove the Jacquet conjecture. With this approach, the Jacquet conjecture is proved under an assumption which is then verified in several cases, including the case of level zero representations.
Original language  English 

Pages (fromto)  9911007 
Number of pages  17 
Journal  Journal of the European Mathematical Society 
Volume  17 
Issue number  4 
DOIs  
Publication status  Published  Apr 2015 
Profiles

Shaun Stevens
 School of Engineering, Mathematics and Physics  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