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 numbers.

Richard E Borcherds
Representation theory
abelian group
character table

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14:40 - Either the integral should be from 0 to 2pi or from -pi to pi, for you should add a factor of 2pi to inx and imx in the exponent. Otherwise this equality is not true.

newwaveinfantry

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