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 0-1sequence $a$, an irreducible unitary representation $k_a$ of $G$. Every two representations $k_a$ and $k_b$ are weakly equivalent. They are unitarily equivalent if and only if $a$ and $b$ are tail equivalent. Each $k_a$ appears as the Koopman representation associated with some ergodic $G$-quasi-invariant measure (of infinite product type) on the boundary of the tree. Joint work with A. Dudko.
Meeting ID: 852 4277 3200 Passcode: 103121