A unified proof of the Howe-Moore property

2014/03/02 by Ciobotaru, Corina · 1 citation
#20E42 #22D10 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1403.0223

Abstract

We provide a unified proof of all known examples of locally compact groups that enjoy the Howe-Moore property, namely, the vanishing at infinity of all matrix coefficients of the group unitary representations that are without non-zero invariant vectors. These examples are: connected, non-compact, simple real Lie groups with finite center, isotropic simple algebraic groups over non Archimedean local fields and closed, topologically simple subgroups of Aut(T) that act 2-transitively on the boundary at infinity of T, where T is a bi-regular tree with valence > 2 at every vertex.

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