On the Jacquet Conjecture on the Local Converse Problem for p-adic GL_n

2014/09/16 by Moshe Adrian, Baiying Liu, Adrian, Moshe +5 · 2 citations
Mathematics · #22E50 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:22E50

paper · pdf · doi:10.48550/arxiv.1409.4790

15 pages

arxiv created 2014/09/16 · arxiv updated 2014/09/18

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.

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• On the Local Langlands Functoriality Transfer From SO(5) to GL(4)
• On the Local Converse Theorem for Depth (1)/(N) Supercuspidal Representations of GL(2N, F)

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