On unitary representations of algebraic groups over local fields

2020/03/04 by Bekka, Bachir, Echterhoff, Siegfried · 1 citation
#20G05 #22D10 #22D25 #22E50 #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2003.02297

Abstract

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

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• The type I dichotomy for two-step nilpotent locally compact groups

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