## 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 GL_{n} (F ), with F a non-archimedean local field, where τ runs 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, . . . , [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 language | English (US) |
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Pages (from-to) | 991-1007 |

Number of pages | 17 |

Journal | Journal of the European Mathematical Society |

Volume | 17 |

Issue number | 4 |

DOIs | |

State | Published - 2015 |

### Bibliographical note

Publisher Copyright:© European Mathematical Society 2015.

## Keywords

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

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