On unitary representations of algebraic groups over local fields

Author:

Bekka Bachir,Echterhoff Siegfried

Abstract

Let G \mathbf {G} be an algebraic group over a local field k \mathbf {k} of characteristic zero. We show that the locally compact group G ( k ) \mathbf {G}(\mathbf {k}) consisting of the k \mathbf {k} -rational points of G \mathbf {G} is of type I. Moreover, we complete Lipsman’s characterization of the groups G \mathbf {G} for which every irreducible unitary representation of G ( k ) \mathbf {G}(\mathbf {k}) is a CCR representation and show at the same time that such groups belong to the family of trace class groups, recently studied by Deitmar and van Dijk.

Publisher

American Mathematical Society (AMS)

Subject

Mathematics (miscellaneous)

Reference32 articles.

1. New Mathematical Monographs;Bekka, Bachir,2008

2. All reductive 𝔭-adic groups are of type I;Bernšteĭn, I. N.;Funkcional. Anal. i Prilo\v{z}en.,1974

3. Draft of: Representations of 𝑝-adic groups.;Bernšteĭn, I. N.,1992

4. Graduate Texts in Mathematics;Borel, Armand,1991

5. Théorèmes de finitude en cohomologie galoisienne;Borel, A.;Comment. Math. Helv.,1964

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1. Finite central extensions of type I;Representation Theory of the American Mathematical Society;2023-11-21

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