Representation theory: Abelian groups
This lecture discusses the complex representations of finite abelian groups.
We show that any group is iomorphic to its dual (the group of 1-dimensional representations, and isomorphic to its double dual in a canonical way (Pontryagin duality).
We check the orthogonality relations for the character table.
Finally we give a few examples to show the extra complications one gets if we drop the assumption that the group is finite or the field is the complex numbers.