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arXiv · 1904.00953

On a generalization of the Howe-Moore property

Antoine Pinochet Lobos
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Abstract

We define a Howe-Moore property relative to a set of subgroups. Namely, a group $G$ has the Howe-Moore property relative to a set $\mathcal{F}$ of subgroups if for every unitary representation $\pi$ of $G$, whenever the restriction of $\pi$ to any element of $\mathcal{F}$ has no non-trivial invariant vectors, the matrix coefficients vanish at infinity. We prove that a semisimple group has the Howe-Moore property relatively to the family of its factors.

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Antoine Pinochet Lobos. 2019-04-01. On a generalization of the Howe-Moore property. https://arxiv.org/abs/1904.00953

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