Abstract
We extend to non quasi-split orthogonal and unitary groups over a local field some results of J. Arthur and the first author established in the quasi-split case. In particular, we obtain a full Langlands classification for tempered representations in the p-adic case. Using Aubert-Schneider-Stuhler involution, we deduce from this a multiplicity one result for unipotent packets, and by global methods, the same result for unipotent packets in the archimedean case.
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References
J. Arthur, On local character relations. Sel. Math. 2(4), 501–579 (1996)
J. Arthur, Stabilisation of the trace formula III, proof of the main theorems. Ann. Math. (2) 158(3), 769–873 (2003)
J. Arthur, A note on L-packets. Pure Appl. Math. Q. 2(1), 199–217 (2006) (Special Issue: In honor of John H. Coates, Part 1 of 2)
J. Arthur, The Endoscopic Classification of Representations. Orthogonal and Symplectic Groups. AMS Colloquium Publications, vol. 61 (American Mathematical Society, Providence, 2013), 590 p.
D. Goldberg, Reducibility of induced representations for Sp(2n) and SO(n). Am. J. Math. 116(5), 1101–1151 (1994)
K. Hiraga, On functoriality of Zelevinsky involution. Compos. Math. 140, 1625–1656 (2004)
T. Kaletha, A. Minguez, S.W. Shin, P.J. White, Endoscopic classification of representations: inner forms of unitary groups(2014, prépublication), 220 p. arXiv:1409.3731
B. Lemaire, C. Moeglin, J.-L. Waldspurger, Le lemme fondamental pour lŠendoscopie tordue: réduction aux éléments unités. arXiv 1506.03383
C. Moeglin, Sur la classification des séries discrètes des groupes classiques p-adiques: paramètres de Langlands et exhaustivité. J. Eur. Math. Soc. 4, 143–200 (2002)
C. Moeglin, Sur certains paquets d’Arthur et involution d’Aubert-Schneider-Stuhler généralisée. Represent. Theory 10, 86–129 (2006)
C. Moeglin, Multiplicité un dans les paquets dŠArthur aux places p-adiques, in On Certain L-Functions, Clay Mathematics Proceedings, vol. 13 (2011), pp. 333–374. In honor of F. Shahidi
C. Moeglin, Paquets stables des séries discrètes accessibles par endoscopie tordue; leur paramètre de Langlands. Contemp. Math. 614, 295–336 (2014)
C. Moeglin, Paquets d’Arthur spéciaux unipotents aux places archimédiennes et correspondance de Howe, in Representation Theory, Number Theory, and Invariant Theory: In Honor of Roger Howe on the Occasion of His 70th Birthday, ed. by J.-L. Kim, J. Cogdell, C.-B. Zhu. Progress in Mathematics (Birkhauser, Basel, 2017)
C. Moeglin, D. Renard, Paquets d’Arthur des groupes classiques complexes. Contemp. Math. 691, 203–256 (2017)
C. Moeglin, D. Renard, Sur les paquets d’Arthur des groupes classiques réels. J. Eur. Math. Soc. (à paraître)
C. Moeglin, M. Tadic, Construction of discrete series for classical p-adic groups. JAMS 15, 715–786 (2002)
C. Moeglin, J.-L. Waldspurger, Stabilisation de la formule des traces tordue. Progress in Mathematics, vols. 316 and 317 (Birkhäuser Boston, Boston, 2016)
O. Taïbi, Arthur’s multiplicity formula for certain inner forms of special orthogonal and symplectic groups. J. Eur. Math. Soc. (to appear)
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Moeglin, C., Renard, D. (2018). Sur les paquets d’Arthur des groupes classiques et unitaires non quasi-déployés. In: Heiermann, V., Prasad, D. (eds) Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms. Lecture Notes in Mathematics, vol 2221. Springer, Cham. https://doi.org/10.1007/978-3-319-95231-4_8
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DOI: https://doi.org/10.1007/978-3-319-95231-4_8
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