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math.RT2015
On spectra of Koopman, groupoid and quasi-regular representations
Artem Dudko, Rostislav Grigorchuk
In this paper we investigate relations between Koopman, groupoid and quasi-regular representations of countable groups. We show that for an ergodic measure class preserving action…
math.RT2015
On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups
Artem Dudko, Rostislav Grigorchuk
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 tha…
math.RT2014
On diagonal actions of branch groups and the corresponding characters
Artem Dudko, Rostislav Grigorchuk
We introduce notions of absolutely non-free and perfectly non-free group actions and use them to study the associated unitary representations. We show that every weakly branch grou…