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Journal of the London Mathematical Society 2004 70(2):356-368; doi:10.1112/S0024610704005617
© 2004 by London Mathematical Society
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© The London Mathematical Society

Injectivity, Projectivity and Supercuspidal Representations

Jeffrey D. Adler and Alan Roche

Department of Theoretical and Applied Mathematics, University of Akron Akron, OH 44325-4002, USA, adler{at}uakron.edu
Department of Mathematics, University of Oklahoma Norman, OK 73019-0315, USA, aroche{at}math.ou.edu

Received 30 September 2003.

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.


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