| Résume | 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. |
