Journal of Lie Theory

no. 1
A Unified Proof of the Howe-Moore Property
Journal of Lie Theory, Volume 25 (2015) no. 1, pp. 65-89
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.
DOI: 10.5802/jolt.828
Classification: 22D10, 20E42
Keywords: Unitary representations, groups acting on Euclidean buildings, the Howe-Moore property 
@article{JOLT_2015_25_1_a4,
     author = {C. Ciobotaru},
     title = {A {Unified} {Proof} of the {Howe-Moore} {Property}},
     journal = {Journal of Lie Theory},
     pages = {65--89},
     year = {2015},
     volume = {25},
     number = {1},
     doi = {10.5802/jolt.828},
     zbl = {1315.22005},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.828/}
}
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C. Ciobotaru. A Unified Proof of the Howe-Moore Property. Journal of Lie Theory, Volume 25 (2015) no. 1, pp. 65-89. doi: 10.5802/jolt.828

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