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On irreducibility of Koopman representations of Higman-Thompson groups

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Type
Preprint
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Submission Date
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arXiv ID: 1512.02687
Source
arXiv
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Abstract

We introduce a notion of measure contracting actions and show that Koopman representations corresponding to ergodic measure contracting actions are irreducible. As a corollary we obtain that Koopman representations associated to canonical actions of Higman-Thompson groups are irreducible. We also show that the actions of weakly branch groups on the boundaries of rooted trees are measure contracting. This gives a new point of view on irreducibility of the corresponding Koopman representations.

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