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Complementary Series for Hermitian Quaternionic Groups

Published online by Cambridge University Press:  20 November 2018

Goran Muić
Affiliation:
Department of Mathematics University of Utah Salt Lake City, Utah 84112 U.S.A., email: [email protected]
Gordan Savin
Affiliation:
Department of Mathematics University of Utah Salt Lake City, Utah 84112 U.S.A., email: [email protected]
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Abstract

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Let $G$ be a hermitian quaternionic group. We determine complementary series for representations of $G$ induced from super-cuspidal representations of a Levi factor of the Siegel maximal parabolic subgroup of $G$.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2000

References

[Be] Bernstein, J., Draft of: Representations of p-adic groups. (Lectures at Harvard University), written by Karl E. Rumelhart, 1992.Google Scholar
[DKV] Deligne, P., Kazhdan, D. and Vignéras, M. F., Représentations des algèbres centrales simples p-adiques. Représentations des Groupes Réductifs sur un Corps Local, Herman, Paris, 1984, 33–117.Google Scholar
[F] Flicker, Y. Z., Rigidity for automorphic forms. J. Analyse Math. 49 (1987), 135202.Google Scholar
[FK] Flicker, Y. Z. and Kazhdan, D. A., A simple trace formula. J. Analyse Math. 50 (1988), 189200.Google Scholar
[Go] Goldberg, D., Some results on reducibility for unitary groups and local Asai L-functions. J. Reine Angew. Math. 448 (1994), 6595.Google Scholar
[J] Jacquet, H., Principal L-functions of the linear group. Proc. Sympos. Pure Math. 33 (1979), 6386.Google Scholar
[MR] Murnaghan, F. and Repka, J., Reducibility of some induced representations of split classical p-adic groups. Comp.Math., to appear.Google Scholar
[MW] Moeglin, C. and Waldspurger, J. L., Spectral Decomposition and Eisenstein series, une paraphrase de l’Ecriture. Cambridge University Press 133, 1995.Google Scholar
[Si] Silberger, A. J., Introduction to harmonic analysis on reductive p-adic groups. Math. Notes 23, Princeton University Press, Princeton, NJ, 1979.Google Scholar
[Si1] Silberger, A. J., Special representations of reductive p-adic groups are not integrable. Ann. of Math. 111 (1980), 571587.Google Scholar
[Sh1] Shahidi, F., Twisted endoscopy and reducibility of induced representations for p-adic groups. DukeMath. J. 66 (1992), 141.Google Scholar
[Sh2] Shahidi, F., A proof of Langland's conjecture on Plancherel measures; Complementary series for p-adic groups. Ann. of Math. 132 (1990), 273330.Google Scholar
[Sh3] Shahidi, F., Langland's conjecture on Plancherel measures for p-adic groups. Progr. Math. 101 (1991), 277295.Google Scholar
[T] Tadíc, M., Induced representations of GL(n, A) for p-adic division algebras A. J. Reine Angew. Math. 405 (1990), 4877.Google Scholar
[We] Weil, A., Basic Number Theory. Springer Verlag, 1973.Google Scholar
[Ze] Zelevinsky, A. V., Induced representations of reductive p-adic groups, II: On irreducible representations of GL(n). Ann. Sci. École Norm. Sup. 13 (1980), 165210.Google Scholar