Abstract
The purpose of this paper is to report on recent joint work with C.J. Bushnell which forms part of our ongoing program of understanding the category of smooth (complex) representations of a p-adic group in terms of certain irreducible representations of compact, open subgroups. Motivation for this program comes from two special cases which may be viewed as extreme examples of what one hopes is a general phenomenon.
The research for this paper was partially supported, at various times, by SERC grant GR/H26901, EPSRC grant GR/K81584, NSF grant DMS-9003213, a University of Iowa Faculty Scholarship, and by the hospitality of IHES and the Universities of Paris VII and XI.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P.N. Anh and L. Marki, Morita equivalence for rings without identity. Tsukuba J. Math. 11 (1987), 1–16.
J.-N. Bernstein (rédigé par P. Deligne), Le “centre” de Bernstein. Représentations des groupes réductifs sur un corps local. Paris, 1984, pp. 1–32.
F. Borceux, Handbook of categorical algebra 1: Basic category theory, Cambridge University Press 1994
A. Borel, Admissible representations of a semisimple group with vectors fixed under an Iwahori subgroup. Invent. Math. 35 (1976), 233–259.
C.J. Bushnell and P. C. Kutzko, The admissible dual of GL(N) via compact open subgroups. Annals of Math. Studies 129, Princeton University Press 1993.
C.J. Bushnell and P.C. Kutzko, The admissible dual SL(N) I. Ann. Scient. Éc. Norm. Sup. (4) 26 (1993), 261–279.
C.J. Bushnell and P.C. Kutzko, The admissible dual SL(N) II. Proc. London Math. Soc. (3) 68 (1992), 317–379.
C.J. Bushnell and P.C. Kutzko, Smooth representations of reductive p-adic groups. Preprint, 1995.
P. Cartier, Representations of p-adic groups: a survey. Automorphic forms, representations and L-functions (A. Borel & W. Casselman edd.), Proc. Symp. in Pure Math. XXXIII (AMS, Providence, 1979), 111–156.
W. Casselman, Introduction to the theory of admissible representations of p-adic reductive groups. Preprint 1974.
W. Casselman, The unramified principal series of p-adic groups I. Compositio Math. 40 (1980), 387–406.
R.E. Howe, Some qualitative results on the representation theory of GL n over ap-adic field. Pacific J. Math. 73 (1977), 479–538.
R.E. Howe and A. Moy, Hecke algebra isomorphisms for GL(n) over a p-adic field. J. Alg. 131 (1990), 388–424.
D. Kazhdan and G. Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras. Invent. Math. 87 (1987), 153–215.
P.C. Kutzko and A. Moy, On the local Langlands conjecture in prime dimension. Ann. Math. 121 (1985), 495–517.
G. Lusztig, Classification of unipotent representations of simple p-adic groups. Preprint.
M.F. Vigneras Représentations l-modulaires un groupe réductif p-adique avec l ≠p, Birkhäuser, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Birkhäuser Boston
About this chapter
Cite this chapter
Kutzko, P.C. (1998). Smooth Representations of Reductive p-adic Groups. In: Tirao, J., Vogan, D.A., Wolf, J.A. (eds) Geometry and Representation Theory of Real and p-adic groups. Progress in Mathematics, vol 158. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4162-1_10
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4162-1_10
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8681-3
Online ISBN: 978-1-4612-4162-1
eBook Packages: Springer Book Archive