On irreducibility of Koopman representations of Higman-Thompson groups

2015/12/08 by Artem Dudko, Dudko, Artem
Mathematics · #20C15 #37A15 #Dynamical Systems (math.DS) #FOS: Mathematics #Representation Theory (math.RT) #math.DS #math.RT #msc:20C15 #msc:37A15

paper · pdf · doi:10.48550/arxiv.1512.02687

arXiv admin note: text overlap with arXiv:1508.05452

arxiv created 2016/01/17 · arxiv updated 2016/01/19

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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