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INJECTIVITY, PROJECTIVITY AND SUPERCUSPIDAL REPRESENTATIONS

Published online by Cambridge University Press:  01 October 2004

JEFFREY D. ADLER  and
ALAN ROCHE
JEFFREY D. ADLER
Affiliation:
Department of Theoretical and Applied Mathematics, University of Akron, Akron, OH 44325-4002, USAadler@uakron.edu
ALAN ROCHE
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, OK 73019-0315, USAaroche@math.ou.edu
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Abstract

Let $G$ be a reductive $p$-adic group. Consider the category of smooth (complex) representations of $G$ in which a (fixed) closed cocompact subgroup of the centre acts by a (fixed) character. It is well known that the supercuspidal representations in this category are both injective and projective. It is shown that, conversely, an admissible injective or projective object is necessarily supercuspidal.

Keywords

22E5020G05
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 70 , Issue 2 , October 2004 , pp. 356 - 368
Copyright
The London Mathematical Society 2004

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