The Peter-Weyl Theorem for Compact Groups

Abstract

This thesis discusses the Peter-Weyl theorem on compact Hausdorff groups which generalises the classical Plancherel theorem on the circle group S 1 . We also provide explicit calculations to decompose L 2 (G) into irreducible unitary representations for the SU (2) group. Additionally, we state and briefly outline the Gelfand-Raikov The- orem, which states that irreducible unitary representations of locally compact groups separate points.