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

Moshe Adrian, Baiying Liu, Shaun Stevens, Peng Xu

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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 languageEnglish
Pages (from-to)1-13
JournalRepresentation Theory
Volume20
DOIs
Publication statusPublished - 27 Jan 2016

Keywords

  • Local converse problem
  • Special pairs of Whittaker functions

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