Representation Theory

These notes are designed for students in the honours year who have a good grounding in both group theory and linear algebra.

We confine ourselves to classical representation theory, that is, over C. This field has several useful properties which simplify the development. But instead of studying the representations themselves, we focus on their characters, the traces of the corresponding matrices, and these, in turn, can prove very useful for developing group theory. The Fundamental Theorem of Characters is a deep theorem, but can be readily obtained from the Wedderburn Structure Theorem.

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