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THE ALGEBRAIC THEORY OF TEMPERED REPRESENTATIONS OF p-ADIC GROUPS I. PARABOLIC INDUCTION AND RESTRICTION

Published online by Cambridge University Press:  21 September 2006

Peter Schneider  and
Ernst-Wilhelm Zink
Peter Schneider
Affiliation:
Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany (pschnei@math.uni-muenster.de)
Ernst-Wilhelm Zink
Affiliation:
Institut für reine Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany (zink@mathematik.hu-berlin.de)
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Abstract

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In this paper we study the category of non-degenerate modules over the Harish-Chandra Schwartz algebra of a p-adic connected reductive group. We construct functors of parabolic induction and restriction and show that they are exact and both ways adjoint to each other.

Keywords

p-adic reductive groupSchwartz algebratempered representationPrimary 22E50
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 6 , Issue 4 , October 2007 , pp. 639 - 688
Copyright
2006 Cambridge University Press