Towards the Jacquet conjecture on the local converse problem for p-adic GL(n)

Jiang, Dihua, Nien, Chufeng and Stevens, Shaun (2015) Towards the Jacquet conjecture on the local converse problem for p-adic GL(n). Journal of the European Mathematical Society, 17 (4). pp. 991-1007. ISSN 1435-9855

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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 non-archimedean 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.

Item Type:	Article
Additional Information:	Authors' final version before typesetting; first published in the Journal of the European Mathematical Society in volume 17 (2015), published by the European Mathematical Society.
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Number Theory (former - to 2017) Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	Pure Connector
Date Deposited:	09 Jul 2014 12:08
Last Modified:	12 Dec 2024 01:37
URI:	https://ueaeprints.uea.ac.uk/id/eprint/48819
DOI:	10.4171/JEMS/524

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