Unitary representations and the type I property of groups acting on trees

Abstract: Unitary representations are a classical and useful tool for studying locally compact groups: motivated in part by quantum mechanics, they have been studied in detail since the early-mid 1900’s with much success, and they enable group theorists to employ functional analytic techniques in the study of locally compact groups. The algebras that unitary representations generate play an important role in not only understanding the representation theory of a locally compact group, but also in understanding properties pertaining to the group itself. This talk will give a brief introduction to some of the basics of the unitary representation theory of locally compact groups, with focus placed on the associated operator algebraic structures/properties. In particular, `type I groups' and `CCR groups' will be the main focus. As an application, I will discuss some current research interests in the unitary representation theory of groups acting on trees, including work of myself on the unitary representation theory of `scale groups’.

group theory

Audience: researchers in the discipline

Symmetry in Newcastle