Abstract
In earlier work, we proved that any quadratic base change automorphic cuspidal representation of GL(n) is distinguished by a unitary group. Here we prove that we can take the unitary group to be quasi-split
Similar content being viewed by others
References
J. Arthur and L. Clozel, Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula, Annals of Mathematics Studies, Vol. 120, Princeton University Press, Princeton, NJ, 1989.
E. M. Baruch, A proof of Kirillov’s conjecture, Annales of Mathematics (2) 158 (2003), 207–252.
J. N. Bernstein, P-invariant distributions on GL(itN) and the classification of unitary representations of GL(N) (non-Archimedean case), in Lie Group Representations, II (College Park, Md., 1982/1983), Lecture Notes in Mathematics, Vol. 1041, Springer, Berlin, 1984, pp. 50–102.
I. M. Gel’fand and D. A. Kajdan, Representations of the group GL(n,K) where K is a local field, in Lie Groups and their Representations (Proc. Summer School, Bolyai János Math. Soc., Budapest, 1971), Halsted, New York, 1975, pp. 95–118.
H. Jacquet, Factorization of period integrals, Journal of Number Theory 87 (2001), 109–143.
H. Jacquet, Transfert lisse d’intégrales de Kloosterman, Comptes Rendus Mathématique, Académie des Sciences, Paris 335 (2002), 229–232.
H. Jacquet, Facteurs de transfert pour les intégrales de Kloosterman., Comptes Rendus Mathématique, Académie des Sciences (2), Paris 336 (2003), 121–124.
H. Jacquet, Smooth transfer of Kloosterman integrals, Duke Mathematical Journal 120 (2003), 121–152.
H. Jacquet, Kloosterman identities over a quadratic extension., Annals of Mathematics (2) 160 (2004), 755–779.
H. Jacquet, Kloosterman identities over a quadratic extension. II, Annales Scientifiques de l’École Normale Supérieure (4) 38 (2005), 609–669.
H. Jacquet, Archimedean Rankin-Selberg integrals, in Automorphic Forms and Lfunctions II. Local aspects, Contemporary Mathematics, Vol. 489, American Mathematical Society, Providence, RI, 2009, pp. 57–172.
H. Jacquet, I. I. Piatetskii-Shapiro and J. A. Shalika, Rankin-Selberg convolutions, American Journal of Mathematics 105 (1983), 367–464.
H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic representations. I, American Journal of Mathematics 103 (1981), 499–558.
H. Jacquet and J. Shalika, A lemma on highly ramified ε-factors, Mathematische Annalen 271 (1985), 319–332.
E. M. Lapid, On the fine spectral expansion of Jacquet’s relative trace formula, Journal of the Institute of Mathematics of Jussieu 5 (2006), 263–308.
N. S. Poulsen, On C ∞-vectors and intertwining bilinear forms for representations of Lie groups, Journal of Functional Analysis 9 (1972), 87–120.
J. A. Shalika, The multiplicity one theorem for GLn, Annals of Mathematics (2) 100 (1974), 171–193.
T. Umeda, Newton’s formula for gln, Proceedings of the American Mathematical Society 126 (1998), 3169–3175.
D. A. Vogan, Jr., Gel’fand-Kirillov dimension for Harish-Chandra modules, Inventiones Mathematicae 48 (1978), 75–98.
D. A. Vogan, Jr., The unitary dual of GL(n) over an Archimedean field, Inventiones Mathematicae 83 (1986), 449–505.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jacquet, H. Distinction by the quasi-split unitary group. Isr. J. Math. 178, 269–324 (2010). https://doi.org/10.1007/s11856-010-0066-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11856-010-0066-1