EVENT DETAILS AND ABSTRACT

Title: A topological boundary for unitary representations of discrete groups
Speaker: Mehrdad Kalantar
Speaker Info: University of Houston
Brief Description:
Special Note:
Abstract:

A unitary representation of a discrete group $G$ on a Hilbert space $H$ is amenable (in the sense of Bekka) if $B(H)$ admits an invariant state (equivalently, an equivariant unital positive idempotent onto $\mathbb{C}$) with respect to the inner action of $G$. If a representation $\pi$ of $G$ is not amenable, there is still a minimal invariant subspace of $B(H)$ that is image of an equivariant unital (completely) positive idempotent on $B(H)$. In the case of the regular representation, this subspace is equivarenlty isomorphic to the algebra of continuous functions on the Furstenberg boundary of $G$. We give some properties, examples and applications of this notion for other classes of unitary representations of $G$. This is joint work with Alex Bearden.