Geodesic
Towards the Jacquet conjecture on the Local Converse Problem for $p$-adic $\mathrm {GL}_n$
Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 991-1007.

Voir la notice de l'article provenant de la source EMS Press

The Local Converse Problem is to determine how the family of the local gamma factors γ(s,π×τ,ψ) characterizes the isomorphism class of an irreducible admissible generic representation π 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=1,2,...,[2n​]. Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture, we formulate a general approach to prove 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.
DOI : 10.4171/jems/524
Classification : 11-XX, 00-XX, 22-XX
Keywords: Irreducible admissible representation, Whittaker model, local gamma factor, local converse theorem 
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     author = {Dihua Jiang and Chufeng Nien and Shaun Stevens},
     title = {Towards the {Jacquet} conjecture on the {Local} {Converse} {Problem} for $p$-adic $\mathrm {GL}_n$},
     journal = {Journal of the European Mathematical Society},
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Dihua Jiang; Chufeng Nien; Shaun Stevens. Towards the Jacquet conjecture on the Local Converse Problem for $p$-adic $\mathrm {GL}_n$. Journal of the European Mathematical Society, Tome 17 (2015) no. 4, pp. 991-1007. doi : 10.4171/jems/524. http://geodesic.mathdoc.fr/articles/10.4171/jems/524/

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