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Dihua Jiang; Baiying Liu

Annales de l’institut Fourier

Towards the Jacquet conjecture on the Local Converse Problem for $p$ -adic ${GL}_{n}$

Dihua Jiang; Chufeng Nien; Shaun Stevens — 2015

Journal of the European Mathematical Society

The Local Converse Problem is to determine how the family of the local gamma factors $γ (s, π \times τ, ψ)$ characterizes the isomorphism class of an irreducible admissible generic representation $π$ 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 $r = 1, 2, ..., [\frac{n}{2}]$ . Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture,...

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

Towards the Jacquet conjecture on the Local Converse Problem for $p$ -adic ${GL}_{n}$