ICTS

Let $G$ be a locally compact group and $\rho$ a unitary representation of $G$ on a separable Hilbert space. Then there is a measure space $(X,S,\mu)$ and a (measurable) family of irreducible unitary representations $\{\rho_x| x\in X\}$ such that $\r$ is the direct integral of the $\{\rho_x| x\in X\}$. This result was obtained by F I Mautner in 1950. In this talk, I will outline a proof of the theorem after introducing the concepts and definitions involved.