A unified proof of the Howe–Moore property
(2014) Journal of Lie Theory — Vol. ?, n° ?, p. ? (2015)
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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'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 a bi-regular tree T, with valence >=3 at every vertex.
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Citations
Ciobotaru, C. G. (2014). A unified proof of the Howe–Moore property. Journal of Lie Theory, ?(?), ? https://hdl.handle.net/2078.5/33745 (Original work published 2015)