volume 1, issue 1, P105-112 1949
DOI: 10.4153/cjm-1949-011-9
View full text
|
|
Share

Abstract: Let G be a compact group. According to the celebrated theorem of Peter-Weyl there exists a complete set of finite-dimensional irreducible unitary representations of G, the completeness meaning that for any group element other than the identity there is a representation sending it into a matrix other than the unit matrix. If G is commutative, the representations are necessarily one-dimensional. It is an immediate consequence of the Peter-Weyl theorem that the converse also holds: if every representation is one-…

expand abstract