Let ρ be a cuspidal representation of , with F a non-archimedean local field, and H a maximal Levi subgroup of . We show that if ρ is H-distinguished, then n is even, and H is isomorphic to .
Soit ρ une représentation cuspidale de , lorsque F est un corps local non archimédien, et H un sous-groupe de Levi maximal de . Nous démontrons que si ρ est distinguée par H, alors n est pair, et H est isomorphe à .
Accepted:
Published online:
Nadir Matringe 1
@article{CRMATH_2012__350_17-18_797_0, 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}, publisher = {Elsevier}, volume = {350}, number = {17-18}, year = {2012}, doi = {10.1016/j.crma.2012.10.003}, language = {en}, }
TY - JOUR AU - Nadir Matringe TI - Cuspidal representations of $ GL(n,F)$ distinguished by a maximal Levi subgroup, with F a non-archimedean local field JO - Comptes Rendus. Mathématique PY - 2012 SP - 797 EP - 800 VL - 350 IS - 17-18 PB - Elsevier DO - 10.1016/j.crma.2012.10.003 LA - en ID - CRMATH_2012__350_17-18_797_0 ER -
%0 Journal Article %A Nadir Matringe %T Cuspidal representations of $ GL(n,F)$ distinguished by a maximal Levi subgroup, with F a non-archimedean local field %J Comptes Rendus. Mathématique %D 2012 %P 797-800 %V 350 %N 17-18 %I Elsevier %R 10.1016/j.crma.2012.10.003 %G en %F CRMATH_2012__350_17-18_797_0
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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.003/
[1] Induced representations of reductive p-adic groups, Ann. Sci. E.N.S., Ser. 4, Volume 10 (1977) no. 4, pp. 441-472
[2] Supercuspidal Gelfand pairs, J. Number Theory, Volume 100 (2003) no. 2, pp. 251-269
[3] Two types of distinguished supercuspidal representations, Int. Math. Res. Not., Volume 35 (2002), pp. 1857-1889
[4] Asai L-functions and Jacquetʼs conjecture, Am. J. Math., Volume 126 (2004) no. 4, pp. 789-820
Cited by Sources:
Comments - Policy