The Peter-Weyl theorem, and non-abelian Fourier analysis on compact groups
Updated: 2011-01-23 15:13:15
Let be a compact group. (Throughout this post, all topological groups are assumed to be Hausdorff.) Then has a number of unitary representations, i.e. continuous homomorphisms to the group of unitary operators on a Hilbert space , equipped with the strong operator topology. In particular, one has the left-regular representation , where we equip with [...]