On the Jacquet Conjecture on the local converse problem for p-adic GL_n

Moshe Adrian; Baiying Liu; Shaun Stevens; Peng Xu

doi:10.1090/ert/476

On the Jacquet Conjecture on the local converse problem for p-adic GL_n

Moshe Adrian, Baiying Liu, Shaun Stevens, Peng Xu

Algebra and Combinatorics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

30 Downloads (Pure)

Abstract

Based on previous results of Jiang, Nien and the third author, we prove that any two minimax unitarizable supercuspidals of GL_N that have the same depth and central character admit a special pair of Whittaker functions. This result gives a new reduction towards a final proof of Jacquet's conjecture on the local converse problem for GL_N. As a corollary of our result, we prove Jacquet's conjecture for GL_N, when N is prime.

Original language	English
Pages (from-to)	1-13
Number of pages	13
Journal	Representation Theory
Volume	20
DOIs	https://doi.org/10.1090/ert/476
Publication status	Published - 27 Jan 2016

Keywords

Local converse problem
Special pairs of Whittaker functions

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10.1090/ert/476

ALSX22Accepted author manuscript, 397 KB
pdfOther version, 202 KB

http://arxiv.org/abs/1409.4790

Shaun Stevens
- Shaun.Stevensuea.acuk
- School of Engineering, Mathematics and Physics - Professor of Mathematics
- Algebra and Combinatorics - Member
Person: Research Group Member, Academic, Teaching & Research

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

Cite this

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AB - Based on previous results of Jiang, Nien and the third author, we prove that any two minimax unitarizable supercuspidals of GL_N that have the same depth and central character admit a special pair of Whittaker functions. This result gives a new reduction towards a final proof of Jacquet's conjecture on the local converse problem for GL_N. As a corollary of our result, we prove Jacquet's conjecture for GL_N, when N is prime.

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On the Jacquet Conjecture on the local converse problem for p-adic GL_n

Abstract

Keywords

Access to Document

Profiles

Shaun Stevens

Projects

Explicit Correspondences in Number Theory.

Cite this