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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- Introduction and Contents
- CHAP01 Background
- CHAP02 Strengthening the Foundations
- CHAP03 Representations of Finite Groups
- CHAP04 Algebras and Modules
- CHAP05 New Characters from Old
- CHAP06 Orthonormality
- CHAP07 Examples of Character Tables
- CHAP08 Frobenius Groups