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Cuspidal representations of reductive p-adic groups are relatively injective and projective

Author: Ralf Meyer
Journal: Represent. Theory 19 (2015), 290-298
MSC (2000): Primary 22E50
Published electronically: December 3, 2015
MathSciNet review: 3430372
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Abstract: Cuspidal representations of a reductive $ p$-adic group $ G$ over a field of characteristic different from $ p$ are relatively injective and projective with respect to extensions that split by a $ U$-equivariant linear map for any subgroup $ U$ that is compact modulo the centre. The category of smooth representations over a field whose characteristic does not divide the pro-order of $ G$ is the product of the subcategories of cuspidal representations and of subrepresentations of direct sums of parabolically induced representations.

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Ralf Meyer
Affiliation: Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstraße 3–5, 37073 Göttingen, Germany

Received by editor(s): April 16, 2015
Received by editor(s) in revised form: November 9, 2015
Published electronically: December 3, 2015
Article copyright: © Copyright 2015 American Mathematical Society