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Jacquet Modules of Parabolically Induced Representations and Weyl Groups

Published online by Cambridge University Press:  20 November 2018

Dubravka Ban
Dubravka Ban*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA email: [email protected]
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Abstract

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The representation parabolically induced from an irreducible supercuspidal representation is considered. Irreducible components of Jacquet modules with respect to induction in stages are given. The results are used for consideration of generalized Steinberg representations.

Keywords

22E50
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 53 , Issue 4 , 01 August 2001 , pp. 675 - 695
Copyright
Copyright © Canadian Mathematical Society 2001

References

[A] Aubert, A.-M., Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d’un groupe réductif p-adique. Trans. Amer. Math. Soc. 347(1995), 2179–2189, and Erratum. ibid. 348(1996), 4687–4690.Google Scholar
[B] Bernstein, J. N., Le ‘centre’ de Bernstein. In: Représentations des groupes réductifs sur un corps local (ed. Deligne, P.), Hermann, Paris, 1984, 1–32.Google Scholar
[BZ] Bernstein, I. N. and Zelevinsky, A. V., Induced representation of reductive p-adic groups, I. Ann. Sci. École Norm. Sup. 10(1977), 441–472.Google Scholar
[Ba1] Ban, D., Parabolic induction and Jacquet modules of representations of O(2n, F) . Glas. Mat. Ser. III 34(54)(1999), 147–185.Google Scholar
[Ba2] Ban, D., Self-duality in the case of SO(2n, F) . Glas. Mat. Ser. III 34(54)(1999), 187–196.Google Scholar
[BoW] Borel, A. and Wallach, N., Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. 2nd edition, Math. Surveys Monographs 67, Amer. Math. Soc., Providence, RI, 2000.Google Scholar
[C] Casselman, W., Introduction to the theory of admissible representations of p-adic reductive groups. Preprint.Google Scholar
[G] Goldberg, D., Reducibility of induced representations for Sp(2n) and SO(n) . Amer. J. Math. 116(1994), 1101–1151.Google Scholar
[J1] Jantzen, C., On square-integrable representations of classical p-adic groups I. Canad. J. Math. 52(2000), 539–581.Google Scholar
[J2] Jantzen, C., On square-integrable representations of classical p-adic groups II. Represent. Theory 4(2000), 127–180.Google Scholar
[J3] Jantzen, C., Degenerate principal series for symplectic and odd-orthogonal groups. Mem. Amer. Math. Soc. 590(1996), 1–100.Google Scholar
[J4] Jantzen, C., Degenerate principal series for orthogonal groups. J. Reine Angew. Math. 441(1993), 61–98.Google Scholar
[MT] Moeglin, C. and Tadić, M., Construction of discrete series for classical p-adic groups. Preprint.Google Scholar
[R] Rodier, F., Décomposition de la série principale des groupes réductifs p-adiques. Non-commutative harmonic analysis (Marseille, 1980), Lecture Notes in Math. 880, Springer-Verlag, Berlin, 1981, 408–424.Google Scholar
[S] Silberger, A., Special representations of reductive groups are not integrable. Ann. of Math. 111(1980), 571–587.Google Scholar
[ScSt] Schneider, P. and Stuhler, U., Representation theory and sheaves on the Bruhat-Tits building. Inst. Hautes Études Sci. Publ. Math. 85(1997), 97–191.Google Scholar
[Sh] 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., Structure arising from induction and Jacquet modules of representations of classical p-adic groups. J. Algebra 177(1995), 1–33.Google Scholar
[T2] Tadić, M., On regular square integrable representations of p-adic groups. Amer. J.Math. 120(1998), 159–210.Google Scholar
[T3] Tadić, M., On reducibility of parabolic induction. Israel J. Math. 107(1998), 29–91.Google Scholar
[Z] Zelevinsky, A. V., Induced representations of reductive p-adic groups, II, On irreducible representations of GL(n) . Ann. Sci. ´ Ecole Norm. Sup. 13(1980), 165–210.Google Scholar