The Peter-Weyl Theorem for Compact Groups

Wednesday, April 29, 2015 - 4:00pm
MSB 312
Andreas Giannopoulos (Advisor: Professor Shuichiro Takeda)

In this talk we will prove the Peter-Weyl theorem for compact groups. First we will show that the matrix coefficients on a compact group G are dense in the space of continuous complex-valued functions on G, and therefore in the space of square-integrable functions, with respect to a Haar measure. Using this, and the direct sum of irreducible representations of G and their dual representations, we will then obtain an isomorphism to the space of square integrable functions on G.