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On the Structure of the Full Lift for the Howe Correspondence of (Sp(n), O(V)) for Rank-One Reducibilities

Published online by Cambridge University Press:  20 November 2018

Goran Muić*
Affiliation:
Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia e-mail: gmuic@math.hr
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Abstract

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In this paper we determine the structure of the full lift for the Howe correspondence of $\left( Sp\left( n \right),O\left( V \right) \right)$ for rank-one reducibilities.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2006

References

[Be] Bernstein, J., Second adjointness for representations of p-adic reductive groups. Preprint (Harvard 1987).Google Scholar
[Be1] Bernstein, J., Draft of: Representations of p-adic groups. (Lectures at Harvard University, 1992, written by Karl E. Rumelhart.)Google Scholar
[BZ] Bernstein, I. N. and Zelevinsky, A. V., Induced representations of reductive p-adic groups. I. Ann. Sci. École Norm Sup. 10(1977), 441472.Google Scholar
[Ca] Casselman, W., Introduction to the theory of admissible representations of p-adic reductive groups. http:www.math.ubc/ca/_cass/research/p-adic-book.dvi Google Scholar
[Go] Goldberg, D., Reducibility of induced representations for Sp(2n) and SO(n). Amer. J. Math. 116(1994), 11011151.Google Scholar
[Ku] Kudla, S. S., On the local theta-correspondence. Invent. Math. 83(1986), 229255.Google Scholar
[Ku1] Kudla, S. S., Notes on the theta correspondence (lectures at European School of Group Theory, 1996). http://www.math.umd.edu/_ssk/castle.pdf Google Scholar
[M] Muić, G., Howe correspondence for discrete series representations; the case of (Sp(n), O(V)). J. Reine Angew. Math. 567(2004), 99150.Google Scholar
[M1] Muić, G., The Howe correspondence and reducibility of induced representations for Sp(n) and O(V). Manuscript (1998).Google Scholar
[M2] Muić, G., The Howe correspondence for non-tempered representations. In preparation.Google Scholar
[MVW] Moeglin, C., Vignéras, M.-F., and Waldspurger, J. L., Correspondence de Howe sur un corps p-adique. Lecture Notes in Math. 1291(1987)Google Scholar
[MR] Murnaghan, F. and Repka, J., Reducibility of some induced representations of split classical p-adic groups. Compositio Math 114(1998), 263313 .Google Scholar
[Ra] Rallis, S., On the Howe duality conjecture. Comp. Math. 51(1984), 333399.Google Scholar
[Sh] Shahidi, F., Twisted endoscopy and reducibility of induced representations for p-adic groups. Duke Math. J. 66(1992), 141.Google Scholar
[Si] Silberger, A. J., Introduction to Harmonic Analysis on Reductive P-Adic Groups. Math. Notes of Princeton University Press, Princeton, 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
[T] Tadić, M., On regular square integrable representations of p-adic groups. Amer. J. Math 120(1998), 159210.Google Scholar
[W] Waldspurger, J.-L., Demonstration d’une conjecture de duality de Howe dans le case p-adiques, p ≠ 2 . In: Festschrift in Honor of I. I. Piatetski-Shapiro, Part II. Israel Math. Conf. Proc. Weizmann, Jerusalem, 1990, pp. 267324.Google Scholar