Seminarium Wydziałowe

Dr hab. Alexandre Danilenko, prof. UMK wygłosi wykład pt. Irreducible Koopman representations for groups of automorphisms of rooted trees.

 

Let G be a countable branch group of automorphisms of a spherically homogeneous rooted tree. Under some assumption on finitarity of G, we construct, for each infinite 0-1 sequence, an irreducible unitary representation of G. Every two representations are weakly equivalent. They are unitarily equivalent if and only if the underlying  0-1 sequences differ only in a finite number of  coordinates.  Each representation appears as the unitary Koopman representation associated with some ergodic G-quasi-invariant measure (of infinite product type) on the boundary of the tree.