A unified proof of the Howe-Moore property

Corina Ciobotaru

A unified proof of the Howe-Moore property

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

10 Citationer (Scopus)

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.

Originalsprog	Engelsk
Tidsskrift	Journal of Lie Theory
Vol/bind	25
Nummer	1
Sider (fra-til)	65-89
Antal sider	25
ISSN	0949-5932
Status	Udgivet - 2014
Udgivet eksternt	Ja

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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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AB - 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.

KW - Groups acting on Euclidean buildings

KW - The Howe-Moore property.

KW - Unitary representations

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A unified proof of the Howe-Moore property

Abstract

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