A unified proof of the howe-moore property

Ciobotaru, Corina
(2014) Journal of Lie Theory — Vol. 25, n° 1, p. 65-89 (2014)

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  • Ciobotaru, CorinaUCLouvain
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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 nonarchimedean local fields and closed, topologically simple subgroups of Aut(T) that act 2-transitively on the boundary θT , where T is a bi-regular tree with valence ≥ 3 at every vertex.
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Ciobotaru, C. (2014). A unified proof of the howe-moore property. Journal of Lie Theory, 25(1), 65-89. https://hdl.handle.net/2078.5/46593 (Original work published 2014)