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Reducibility of Generalized Principal Series

Published online by Cambridge University Press:  20 November 2018

Goran Muić
Goran Muić*
Affiliation:
Department of Mathematics, University of Zagreb, Bijenicka 30, 10000 Zagreb, Croatia, e-mail: [email protected]
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Abstract

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In this paper we describe reducibility of non-unitary generalized principal series for classical $p$-adic groups in terms of the classification of discrete series due to Mœglin and Tadić.

Keywords

22E3522E5011F70
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 3 , 01 June 2005 , pp. 616 - 647
Copyright
Copyright © Canadian Mathematical Society 2005

References

[Ca] Casselman, W., Introduction to the theory of admissible representations of p-adic reductive groups. preprintGoogle Scholar
[J] Jantzen, C., Degenerate principal series for symplectic and odd-orthogonal groups. Mem. Amer. Math. Society 124(1996), 1–100.Google Scholar
[M1] Muić, G., Some results on square integrable representations; Irreducibility of standard representations. Internat.Math. Res. Notices 14(1998), 705–726.Google Scholar
[M2] Muić, G., A proof of Casselman-Shahidi's conjecture for quasi-split classical groups. Canad. Math. Bull. 44(2001), 298–312.Google Scholar
[M3] Muić, G., Howe correspondence for discrete series representations; the case of (Sp(n),O(V)). J. Reine Angew.Math. 567(2004), 99–150.Google Scholar
[M4] Muić, G., Composition series of generalized principal series; the case of strongly positive discrete series. Israel J. Math. 140(2004), 157–202.Google Scholar
[Moe] C.Moeglin, Sur la classification des séries discrètes des groupes classiques p-adiques: paramètres de Langlands et exhaustivité. J. Eur.Math. Soc. 4(2002), 143–200.Google Scholar
[MT] Moeglin, C., and Tadić, M., Construction of discrete series for classical p-adic groups. Amer. J. Math. Soc 15(2002), 715–786.Google Scholar
[MVW] Moeglin, C., Vignéras, M.-F., and Waldspurger, J. L., Correspondence de Howe sur un corps p-adique. Lecture Notes in Mathematics 1291, Springer-Verlag, Berlin, 1987.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., Twisted endoscopy and reducibility of induced representations for p-adic groups. Duke Math. J. 66(1992), 1–41.Google Scholar
[T1] Tadić, M., On reducibility of parabolic induction. Israel J. Math 107(1998), 29–91.Google Scholar
[T2] Tadić, M., Manuscript.Google Scholar
[W] Waldspurger, J.-L., La formule de Plancherel pour les groupes p-adiques, d’après Harish-Chandra. J. Inst. Math. Jussieu 2(2003), 235–333.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. (4) 13(1980), 165–210.Google Scholar