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Reducibility for Non-Connected p-Adic Groups, With G° Of Prime Index

Published online by Cambridge University Press:  20 November 2018

David Goldberg
David Goldberg*
Affiliation:
Department of Mathematics Purdue University West Lafayette, Indiana 47907 U.S.A.
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Abstract

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We determine the structure of representations induced from discrete series of parabolic subgroups of quasi-split p-adic groups G with G/G° a cyclic group of prime order. We attach to each such representation an R-group which extends the definition of the Knapp-Stein R-group. We show that this R-group has the properties predicted by Arthur. We apply our results to the case of Orthogonal groups.

Keywords

22E5022E35
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 2 , 01 April 1995 , pp. 344 - 363
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Arthur, J., On elliptic tempered characters, Acta Math. 171(1993), 73–138.Google Scholar
2. Arthur, J., Intertwining operators and residues I. Weighted characters, J. Funct. Anal. 84(1989), 19–84.Google Scholar
3. Arthur, J., Unipotent automorphic representations: conjectures, Société Mathématique de France, Astérisque 171-172(1989), 13–71.Google Scholar
4. Arthur, J., Unipotent automorphic representations: Global Motivations. In: Automorphic Forms, Shimura Varieties, and L-functions, Vol. I, (eds. Clozel, L. and Milne, J.S.), Perspect. Math. 10, Academic Press, New York, New York, 1990. 1–75.Google Scholar
5. Borel, A., Automorphic L-functions, Proc. Sympos. Pure Math. (2) 33(1979), 27–61.Google Scholar
6. Gelbart, S.S. and Knapp, A.W., L-indistinguishability and R groups for the special linear group, Adv. in Math. 43(1982), 101–121.Google Scholar
7. Goldberg, D., R-groups and elliptic representations for unitary groups, Proc. Amer. Math. Soc, to appear.Google Scholar
8. Goldberg, D., Reducibility of induced representations for Sp(2«) and SO(«), Amer. J. Math. 116(1994), 1101–1151.Google Scholar
9. Goldberg, D., R-groups and elliptic representations for SLn, Pacific J. Math. 165(1994), 77–92.Google Scholar
10. Harish-Chandra, , Harmonic analysis on reductivep-adic groups, Proc. Sympos. Pure Math. 26(1973), 167–192.Google Scholar
11. Herb, R.A., Elliptic representations for Sp(2n) and SO(n), Pacific J. Math. 161(1993), 347–358.Google Scholar
12. Labesse, J.P., Cohomologie, L-groups etfunctorialité, Compositio Math. 55(1984), 163–184.Google Scholar
13. Keys, C.D., L-indistinguishability and R-groups for quasi split groups: unitary groups in even dimension, Ann. Sci. École Norm. Sup. (4) 20(1987), 31–64.Google Scholar
14. Knapp, A.W. and Stein, E.M., Irreducibility theorems for the principal series. In: Conference on Harmonic Analysis, Lecture Notes in Math. 266, Springer-Verlag, New York, Heidelberg, Berlin, 1972. 197–214.Google Scholar
15. Knapp, A.W. and Zuckerman, G., Normalizing factors, tempered representations, and L-groups, Proc. Sympos. Pure Math. (1) 33(1979), 93–105.Google Scholar
16. Langlands, R.P., Representations ofabelian algebraic groups, Yale University, 1968.Google Scholar
17. Shahidi, F., On certain L-functions, Amer. J. Math. (2) 103(1981), 297–355.Google Scholar
18. Shahidi, F., A proof of Langlands conjecture for Plancherel measures; complementary series for p-adic groups Ann. of Math. (2) 132(1990), 273–330.Google Scholar
19. Shelstad, D., L-indistinguishability for real groups Math. Ann. 259(1982), 385–430.Google Scholar
20. Silberger, A.J., The Knapp-Stein dimension theorem for p-adic groups, Proc. Amer. Math. Soc. 68(1978), 243–246.Google Scholar
21. Silberger, A.J., The Knapp-Stein dimension theorem for p-adic groups. Correction Proc. Amer. Math. Soc. 76(1979), 169–170.Google Scholar
22. Silberger, A.J., Introduction to Harmonic Analysis on Reductive p-adic Groups, Math. Notes 23, Princeton University Press, Princeton, New Jersey, 1979.Google Scholar