Abstract
We fix a reductive p-adic group G. One very useful tool in the representation theory of reductive p-adic groups is the Jacquet module. Let us recall the definition of the Jacquet module. Let (π, V) be a smooth representation of G and let P be a parabolic subgroup of G with a Levi decomposition P = MN. The Jacquet module of V with respect to N is \( {V_N} = V/spa{n_{\mathbb{C}}}\left\{ {\pi (n)v - v;n \in N,v \in V} \right\} \).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J. Bernstein, P. Deligne, and D. Kazhdan, Trace Paley-Wiener theorem for reductive p-adic groups, J. Analyse Math 47 (1986), 180–192.
J. Bernstein and A.V. Zelevinsky, Induced representations of reductive p-adic groups I, Ann. Sci. École Norm. Sup. 10 (1977), 441–472.
W. Casselman, Intro, to the theory of admisssible representations, preprint.
P. Deligne, D. Kazhdan, M.-F. Vigneras, Representations des algebres centrales simples p-adiques, Representations des Groupes Reductifs sur un Corps Local, Hermann, Paris, 1984.
D. K. Faddeev, On multiplication of representations of classical groups over a finite field with representations of the full linear group, Vestnik Lenigradskogo Universiteta 13 (1976), 35–40. (Russian)
R. Gustafson, The degenerate principal series for Sp(2n), Memoirs of the AMS 248 (1981).
F. Rodier, Décomposition de la série principale des groupes réductifs p-adiques, Non-Commutative Harmonic Analysis, Lecture Notes in Mathematics, Vol. 880, Springer-Verlag, Berlin-Heidelberg-New York, 1981.
F. Rodier, Sur les representations non ramifiees des groupes reductifs p-adiques; Vexample de GSp(4), Bull. Soc. Math. France 116 (1988), 15–42.
P. J. Sally, M. Tadic, On representations of non-archimedean GSp(2), manuscript.
F. Shahidi, A proof of Langlands conjecture on Plancherel measure; comple-mentary series for p-adic groups, Annals of Math (2) 132 (1990), 273–330.
F. Shahidi, Langlands’ conjecture on Plancherel measures for p-adic groups, these proceedings.
M. Tadic, Induced representations of GL(n,A) for p-adic division algebras A, J. reine angew. Math. 405 (1990), 48–77.
J.-L. Waldspurger, Un exercice sur GSp(4, F) et les representations de Weil, Bull. Soc. Math.France 115 (1987), 35–69.
A. V. Zelevinsky, Induced representations of reductive p-adic groups II, On irreducible representations of GL(n), Ann. Sci. École Norm. Sup. 13 (1980), 165–210.
A. V. Zelevinsky, Representations of Finite Classical Groups, A Hopf Algebra Approach, Lecture Notes in Math., Vol. 869, Springer-Verlag, Berlin-Heidelberg-New York, 1981.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media New York
About this chapter
Cite this chapter
Tadić, M. (1991). On Jacquet Modules of Induced Representations of p—Adic Symplectic Groups. In: Barker, W.H., Sally, P.J. (eds) Harmonic Analysis on Reductive Groups. Progress in Mathematics, vol 101. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0455-8_16
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0455-8_16
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6768-3
Online ISBN: 978-1-4612-0455-8
eBook Packages: Springer Book Archive