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A Proof of Casselman-Shahidi’s Conjecture for Quasi-split Classical Groups

Published online by Cambridge University Press:  20 November 2018

Goran Muić
Goran Muić*
Affiliation:
Department of Mathematics University of Utah Salt Lake City, UT 84112 USA, e-mail: [email protected]
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Abstract

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In this paper the author prove that standard modules of classical groups whose Langlands quotients are generic are irreducible. This establishes a conjecture of Casselman and Shahidi for this important class of groups.

Keywords

22E35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 3 , 01 September 2001 , pp. 298 - 312
Copyright
Copyright © Canadian Mathematical Society 2001

References

[B] Borel, A., Automorphic L-functions. Part 2, Proc. Symp. Pure Math. 33 (1979), 27–61.Google Scholar
[Ba] Ban, D., Selfduality in the case of SO(2n, F). Glas. Mat. Ser. III, to appear.Google Scholar
[BW] Borel, A. and Wallach, N., Continuous Cohomology, discrete subgroups and representations of reductive groups. Princeton University Press, Princeton, 1980.Google Scholar
[CS] Casselman, W. and Shahidi, F., On irreducibility of standard modules for generic representations. Ann. Sci. E´ cole Norm Sup. 31 (1998), 561–589.Google Scholar
[G] Goldberg, D., Some results on reducibility of induced representations for unitary groups and local Asai L-functions. J. Reine Angew. Math. 448 (1994), 65–95.Google Scholar
[H] Henniart, G., On the local Langlands conjecture for GL(n): the cyclic case. Ann. of Math. 123 (1986), 145–203.Google Scholar
[JPSS] Jacquet, H., Piatetski-Shapiro, I. I. and Shalika, J. A., Rankin-Selberg convolutions. Amer. J. Math. 105 (1983), 367–464.Google Scholar
[KSh] Kimand, H. Shahidi, F., Symmetric cube L-functions for GL2 are entire. Ann. of Math., to appear.Google Scholar
[M] Muić, G., Some results on square integrable representations; Irreducibility of standard representations. Internat.Math. Res. Notices 14 (1998), 705–726.Google Scholar
[M1] Muić, G., On generic irreducible representations of Sp(n, F) and SO(2n + 1, F). Glas. Mat. Ser. III 33(55)(1998), 19–31.Google Scholar
[MS] Muić, G. and Savin, G., Symplectic-orthogonal theta lifts of generic discrete series. Duke Math. J., to appear.Google Scholar
[MSh] Muić, G. and Shahidi, F., Irreducibility of standard representations for Iwahori-spherical representations. Math. Ann. 312 (1998), 151–165.Google Scholar
[Sh1] Shahidi, F., A proof of Langland's conjecture on Plancherel measures; Complementary series for p-adic groups. Ann. of Math. 132 (1990), 273–330.Google Scholar
[Sh2] Shahidi, F., On multiplicativity of local factors. In: Festschrift in Honor of I. I. Piatetski-Shapiro, Part II, Israel Math. Conf. Proc. 3, Weizmann, Jerusalem, 1990, 226–242.Google Scholar
[Sh3] Shahidi, F., Twisted endoscopy and reducibility of induced representations for p-adic groups. Duke Math. J. 66 (1992), 1–41.Google Scholar
[Sh4] Shahidi, F., Fourier transforms of intertwining operators and Plancherel measures for GL(n). Amer. J. Math. 106 (1984), 67–111.Google Scholar
[Si] Silberger, A. J., Introduction to harmonic analysis on reductive p-adic groups. Math. Notes, Princeton University Press, Princeton, 1979.Google Scholar
[T] Tadić, M., On regular square integrable representations of p-adic groups. Amer. J. Math 120 (1998), 159–210.Google Scholar
[Z] Zhang, Y., The holomorphy and non-vanishing of normalized intertwining operators. Pacific J. Math 180 (1997), 385–398.Google Scholar
[Ze] Zelevinsky, A. V., Induced representations of reductive p-adic groups. On irreducible representations of GL(n). Ann. Sci. E´ cole Norm. Sup. 13 (1980), 165–210.Google Scholar