Number Theory/Group Theory
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.

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

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

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DOI: 10.1016/j.crma.2012.10.003
Matringe, Nadir 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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Matringe, Nadir. 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. http://www.numdam.org/articles/10.1016/j.crma.2012.10.003/

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

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

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

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

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