Number theory
On the relationship between distinction and irreducibility of parabolic induction
Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 827-831.

Let U2n denote the quasi-split unitary group over 2n variables with respect to a quadratic extension E/F of p-adic fields. In this short note, we relate GLn(F)-distinction of ladder representations of GLn(E) with irreducibility of its Siegel parabolic induction in U2n.

Soit U2n le groupe unitaire quasi déployé à 2n variables associé à une extension E/F de corps p-adiques. Dans cette courte note, nous établissons un lien entre la propriété de distinction par GLn(F) d'une représentation en échelle de GLn(E) et l'irréductibilité de son induite parabolique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.10.009
Mitra, Arnab 1

1 Indian Institute of Science Education and Research Tirupati, India
@article{CRMATH_2019__357_11-12_827_0,
     author = {Mitra, Arnab},
     title = {On the relationship between distinction and irreducibility of parabolic induction},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {827--831},
     publisher = {Elsevier},
     volume = {357},
     number = {11-12},
     year = {2019},
     doi = {10.1016/j.crma.2019.10.009},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2019.10.009/}
}
TY  - JOUR
AU  - Mitra, Arnab
TI  - On the relationship between distinction and irreducibility of parabolic induction
JO  - Comptes Rendus. Mathématique
PY  - 2019
SP  - 827
EP  - 831
VL  - 357
IS  - 11-12
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2019.10.009/
DO  - 10.1016/j.crma.2019.10.009
LA  - en
ID  - CRMATH_2019__357_11-12_827_0
ER  - 
%0 Journal Article
%A Mitra, Arnab
%T On the relationship between distinction and irreducibility of parabolic induction
%J Comptes Rendus. Mathématique
%D 2019
%P 827-831
%V 357
%N 11-12
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2019.10.009/
%R 10.1016/j.crma.2019.10.009
%G en
%F CRMATH_2019__357_11-12_827_0
Mitra, Arnab. On the relationship between distinction and irreducibility of parabolic induction. Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 827-831. doi : 10.1016/j.crma.2019.10.009. http://www.numdam.org/articles/10.1016/j.crma.2019.10.009/

[1] Anandavardhanan, U.K.; Kable, A.C.; Tandon, R. Distinguished representations and poles of twisted tensor L-functions, Proc. Amer. Math. Soc., Volume 132 (2004) no. 10, pp. 2875-2883

[2] Anandavardhanan, U.K.; Rajan, C.S. Distinguished representations, base change, and reducibility for unitary groups, Int. Math. Res. Not., Volume 14 (2005), pp. 841-854

[3] Flicker, Y.Z. On distinguished representations, J. Reine Angew. Math., Volume 418 (1991), pp. 139-172

[4] Flicker, Y.Z. Distinguished representations and a Fourier summation formula, Bull. Soc. Math. Fr., Volume 120 (1992) no. 4, pp. 413-465

[5] Goldberg, D. Some results on reducibility for unitary groups and local Asai L-functions, J. Reine Angew. Math., Volume 448 (1994), pp. 65-95

[6] Gurevich, M. On a local conjecture of Jacquet, ladder representations and standard modules, Math. Z., Volume 281 (2015) no. 3–4, pp. 1111-1127

[7] Gurevich, M.; Ma, J.; Mitra, A. On two questions concerning representations distinguished by the Galois involution, Forum Math., Volume 30 (2018) no. 1, pp. 141-157

[8] Kable, A.C. Asai L-functions and Jacquet's conjecture, Amer. J. Math., Volume 126 (2004) no. 4, pp. 789-820

[9] Lapid, E.; Mínguez, A. On a determinantal formula of Tadić, Amer. J. Math., Volume 136 (2014) no. 1, pp. 111-142

[10] Badulescu, I.; Lapid, E.; Mínguez, A. Une condition suffisante pour l'irréductibilité d'une induite parabolique de GL(m,D), Ann. Inst. Fourier (Grenoble), Volume 63 (2013) no. 6, pp. 2239-2266

[11] Lapid, E.; Tadić, M. Some results on reducibility of parabolic induction for classical groups, Amer. J. Math. (2019) (in press) | arXiv

[12] Matringe, N. Distinction of some induced representations, Math. Res. Lett., Volume 17 (2010) no. 1, pp. 77-97

[13] A. Mitra, On certain Sp-distinguished principal series representations of the quasi-split unitary groups, Submitted for publication.

[14] Mitra, A.; Offen, O. On Sp-distinguished representations of the quasi-split unitary groups, J. Inst. Math. Jussieu (2019) | DOI

[15] Prasad, D. On a conjecture of Jacquet about distinguished representations of GL(n), Duke Math. J., Volume 109 (2001), pp. 67-78

[16] Silberger, A. The Langlands quotient theorem for p-adic groups, Math. Ann., Volume 236 (1978) no. 2, pp. 95-104

[17] Tadić, M. Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case), Ann. Sci. Éc. Norm. Supér. (4), Volume 19 (1986) no. 3, pp. 335-382

[18] Zelevinsky, A.V. Induced representations of reductive p-adic groups, II: on irreducible representations of GL(n), Ann. Sci. Éc. Norm. Supér. (4), Volume 13 (1980) no. 2, pp. 165-210

Cited by Sources: