Projects per year
Abstract
We introduce a novel ultrametric on the set of equivalence classes of cuspidal irreducible representations of a general linear group GL(N) over a nonarchimedean local field, based on distinguishability by twisted gamma factors. In the case that N is prime and the residual characteristic is greater than or equal to N/2, we prove that, for any natural number i at most N/2, there are pairs of cuspidal irreducible representations whose logarithmic distance in this ultrametric is precisely i. This implies that, under the same conditions on N, the bound N/2 in the Local Converse Theorem for GL(N) is sharp.
Original language  English 

Pages (fromto)  617 
Number of pages  12 
Journal  Proceedings of the American Mathematical Society, Series B 
Volume  5 
DOIs  
Publication status  Published  20 Feb 2018 
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