Cuspidal representations of $ GL(n,F)$ distinguished by a maximal Levi subgroup, with <i>F</i> a non-archimedean local field

Nadir Matringe

doi:10.1016/j.crma.2012.10.003

Number Theory/Group Theory

Cuspidal representations of

G L (n, F)

distinguished by a maximal Levi subgroup, with F a non-archimedean local field

Presented by: the Editorial Board

Nadir Matringe ¹

¹ Université de Poitiers, laboratoire de mathématiques et applications, téléport 2, BP 30179, boulevard Marie-et-Pierre-Curie, 86962 Futuroscope Chasseneuil cedex, France

Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 797-800

Abstract (Original language)
Résumé

Let ρ be a cuspidal representation of $G L (n, F)$ , with F a non-archimedean local field, and H a maximal Levi subgroup of $G L (n, F)$ . We show that if ρ is H-distinguished, then n is even, and H is isomorphic to $G L (n / 2, F) \times G L (n / 2, F)$ .

Soit ρ une représentation cuspidale de $G L (n, F)$ , lorsque F est un corps local non archimédien, et H un sous-groupe de Levi maximal de $G L (n, F)$ . Nous démontrons que si ρ est distinguée par H, alors n est pair, et H est isomorphe à $G L (n / 2, F) \times G L (n / 2, F)$ .

Received: 2012-07-18
Accepted: 2012-10-02
Published online: 2012-09-01

DOI: 10.1016/j.crma.2012.10.003

Author's affiliations:

Nadir Matringe ¹

¹ Université de Poitiers, laboratoire de mathématiques et applications, téléport 2, BP 30179, boulevard Marie-et-Pierre-Curie, 86962 Futuroscope Chasseneuil cedex, France

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     author = {Nadir Matringe},
     title = {Cuspidal representations of $ GL(n,F)$ distinguished by a maximal {Levi} subgroup, with {\protect\emph{F}} a non-archimedean local field},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {797--800},
     year = {2012},
     publisher = {Elsevier},
     volume = {350},
     number = {17-18},
     doi = {10.1016/j.crma.2012.10.003},
     language = {en},
}

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Nadir Matringe. Cuspidal representations of $ GL(n,F)$ distinguished by a maximal Levi subgroup, with F a non-archimedean local field. Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 797-800. doi: 10.1016/j.crma.2012.10.003

References
Cited by

[1] J.N. Bernstein; A.V. Zelevinsky Induced representations of reductive p-adic groups, Ann. Sci. E.N.S., Ser. 4, Volume 10 (1977) no. 4, pp. 441-472

[2] J. Hakim Supercuspidal Gelfand pairs, J. Number Theory, Volume 100 (2003) no. 2, pp. 251-269

[3] J. Hakim; F. Murnaghan Two types of distinguished supercuspidal representations, Int. Math. Res. Not., Volume 35 (2002), pp. 1857-1889

[4] A.C. Kable Asai L-functions and Jacquetʼs conjecture, Am. J. Math., Volume 126 (2004) no. 4, pp. 789-820

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