Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-19T22:01:41.975Z Has data issue: false hasContentIssue false
  • English
  • Français

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: gmuic@math.utah.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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