Towards the Jacquet conjecture on the Local Converse Problem for p-adic GLn

Dihua Jiang, Chufeng Nien, Shaun Stevens

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

The Local Converse Problem is to determine how the family of the local gamma factors γ (s, π x τ, ψ) characterizes the isomorphism class of an irreducible admissible generic representation τ of GLn (F ), with F a non-archimedean local field, where τ runs through all irreducible supercuspidal representations of GLr (F ) and r runs through positive integers. The Jacquet conjecture asserts that it is enough to take r = 1, . . . , [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 proving 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.

Original languageEnglish (US)
Pages (from-to)991-1007
Number of pages17
JournalJournal of the European Mathematical Society
Volume17
Issue number4
DOIs
StatePublished - 2015

Keywords

  • Irreducible admissible representation
  • Local converse theorem
  • Local gamma factor
  • Whittaker model

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