Search

Throughout this paper, G will denote a compact (Hausdorff) topological group with identity e. When G is abelian, there is no difficulty in relating the group multiplication in G to the multiplication in the dual of G since characters are homomorphisms with respect to pointwise multiplication and pointwise multiplication of characters yields another character. However, in the non-abelian case, there are two multiplications associated with the dual of G: (1) representations are homomorphisms with respect to composition multiplication, and (2) the tensor product of representations yields another representation.