Journal of Lie Theory 25 (2015), No. 1, 065--089
Copyright Heldermann Verlag 2015
A Unified Proof of the Howe-Moore Property
Corina Ciobotaru
Université Catholique de Louvain, IRMP, Chemin du Cyclotron 2, Bte L7.01.02, 1348 Louvain-la-Neuve, Belgique
corina.ciobotaru@uclouvain.be
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's 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 of T, where T is a bi-regular tree with valence ≥3 at every vertex.
Keywords: Unitary representations, groups acting on Euclidean buildings, the Howe-Moore property.
MSC: 22D10, 20E42
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