Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-15T02:13:47.609Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Results on L-Indistinguishability for SL(r)

Published online by Cambridge University Press:  20 November 2018

Freydoon Shahidi
Freydoon Shahidi*
Affiliation:
Purdue University, West Lafayette, Indiana
Rights & Permissions [Opens in a new window]

Extract

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.

Fix a positive integer r. Let AF be the ring of adeles of a number field F. For a parabolic subgroup P of SLr, we fix a Levi decomposition P = MN, and we let

Let be the Weyl group of . It follows from a recent work of James Arthur [1,2] (also cf. [3]) that, among the terms appearing in the trace formula for SLr(AF), coming from the Eisenstein series, are those which are a constant multiple (depending only on M and w) of

1

where σ is a cusp form on M(AF) satisfying wσ ≅ σ,

and

in the notation of [2, 3]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 6 , 01 December 1983 , pp. 1075 - 1109
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Arthur, J., On a family of distributions obtained from Eisenstein series I: Applications of the Paley-Wiener theorem, Amer. J. Math. 104 (1982), 1243–1288.Google Scholar
2. Arthur, J., On a family of distributions obtained from Eisenstein series II: Explicit formulas, Amer. J. Math. 104 (1982), 1289–1336.Google Scholar
3. Arthur, J., The trace formula for reductive groups, Lectures for Journées Automorphes, Dijon University.Google Scholar
4. Casselman, W. and Shalika, J. A., The unramified principal series of p-adic groups II, Comp. Math. 41 (1980), 207–231.Google Scholar
5. Gelbart, S. S. and Knapp, A. W., Irreducible constituents of principal series of SLn(k), Duke Math. J. 48 (1981), 313–326.Google Scholar
6. Gelbart, S. S. and Knapp, A. W., L-indistinguishability and R-groups for the special linear group, Advances in Math. 43 (1982), 101–121.Google Scholar
7. Jacquet, H., From GL2 to GLn, 1975 U. S. -Japan Seminar on Number Theory, Ann Arbor.Google Scholar
8. Jacquet, H., Generic representations (Lecture notes in Math. 587, Springer-Verlag, 1977), 91–101.Google Scholar
9. Jacquet, H., Piatetski-Shapiro, I. I. and Shalika, J. A., Rankin-Selberg convolutions, Amer. J. Math. 705 (1983), 367–464.Google Scholar
10. Knapp, A. W. and Zuckerman, G., Normalizing factors, tempered representations and L-groups, “Automorphic Forms, Representations, and L-functions”, Proc. Symposia Pure Math. 33, Part 1, 93–105 (American Mathematical Society, Providence, R. I., 1979).Google Scholar
11. Labesse, J. P. and Langlands, R. P., L-indistinguishability for SL(2), Can. J. Math. 31 (1979), 726–785.Google Scholar
12. Langlands, R. P., On the functional equations satisfied by Eisenstein series (Lecture notes in Math. 544, Springer-Verlag, 1976).CrossRefGoogle Scholar
13. Langlands, R. P., Les débuts d'une formule des traces stables, printed notes. L'École Normale Supérieure de Jeunes Filles, Paris (1980).Google Scholar
14. Shahidi, F., On certain L-functions, Amer. J. Math. 103 (1981), 297–355.Google Scholar
15. Shahidi, F., Local coefficients and normalization of intertwining operators for GL(n), Comp. Math. 48(1983), 271–295.Google Scholar
16. Shahidi, F., Fourier transforms of intertwining operators and Plancherel measures for GL(n), Amer. J. Math., to appear.CrossRefGoogle Scholar
17. Shelstad, D., Orbital integrals and a family of groups attached to a real reductive group, Ann. Scient. Ec. Norm. Sup. 12 (1979), 1–31.Google Scholar
18. Shelstad, D., L-indistinguishability for real groups, Math. Ann. 259 (1982), 385–430.Google Scholar
19. Silberger, A. J., Introduction to harmonic analysis on reductive p-adic groups, Math. Notes of Princeton University Press 23 (Princeton, N. J., 1979).Google Scholar