engleski

On Jacquet modules of representations of segment type

A new simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra is given in this paper. The first is a proof of the parameterization of the irreducible square integrable representations of these groups by segments of cuspidal representations. The second is a proof of the irreducibility of the tempered parabolic induction. The proofs are based on Jacquet modules (and the Geometric Lemma, incorporated in the structure of a Hopf algebra). Only some very basic general facts of the representation theory of reductive p-adic groups are used in the proofs.

p-adic division algebras ; cuspidal representations ; square integrable representations ; tempered representations ; irreducibility

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