On sharpness in Local Converse Theorems for classical groups and G_2

Adrian, Moshe and Stevens, Shaun (2026) On sharpness in Local Converse Theorems for classical groups and G_2. Advances in Mathematics. ISSN 0001-8708

Preview

PDF (AdrianStevensConverseTheorems) - Accepted Version Download (461kB) | Preview

Abstract

We prove various results about the Local Converse Problem for split reductive groups G over a non-archimedean local field F of characteristic 0 and residual characteristic p. In particular, we prove that when G is a symplectic or special orthogonal group, or the exceptional group G_2, and p is large enough, then the optimal standard Local Converse Theorem for G(F) requires twisting by representations of GL(r,F) with r up to half the dimension of the standard representation of the dual group of G. However, if we restrict to generic supercuspidal representations of G(F) then it can be improved when G = SO(2N); we conjecture that the same is true for symplectic and odd special orthogonal groups. We also consider the possibility of using non-standard representations of the dual group to distinguish representations, giving counterexamples to possible improvements for general linear groups, G_2 and SO(2N).

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	LivePure Connector
Date Deposited:	07 Aug 2026 15:55
Last Modified:	07 Aug 2026 15:56
URI:	https://ueaeprints.uea.ac.uk/id/eprint/104057
DOI:

Downloads

Actions (login required)

View Item