Comptes Rendus
Number theory
On the relationship between distinction and irreducibility of parabolic induction
[Sur la relation entre distinction et irréductibilité de l'induction parabolique]
Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 827-831.

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.

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.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2019.10.009

Arnab Mitra 1

1 Indian Institute of Science Education and Research Tirupati, India
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Arnab Mitra. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.10.009/

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

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

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

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

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

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

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

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

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

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

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

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

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

[17] M. Tadić 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] A.V. Zelevinsky 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

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