On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups

@article{Dudko2015OnIA,
title={On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups},
author={A. Dudko and R. Grigorchuk},
journal={arXiv: Representation Theory},
year={2015}
}

We study Koopman and quasi-regular representations corresponding to the action of arbitrary weakly branch group G on the boundary of a rooted tree T. One of the main results is that in the case of a quasi-invariant Bernoulli measure on the boundary of T the corresponding Koopman representation of G is irreducible (under some general conditions). We also show that quasi-regular representations of G corresponding to different orbits and Koopman representations corresponding to different Bernoulli… Expand