Representation theory Abelian groups

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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 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