Maximilian Niclas Ley: An Overview of Character theory for Finite Groups

Abstract:

Representation theory is a very large branch of mathematics with applications in group theory, physics and many other subjects. This report will give an overview of basic representation theory and take a look at the properties of the characters of a representation. Among the theorems and concepts discussed will be Maschke’s theorem, Schur’s lemma, orthogonality amongst characters, the number of irreducible representations, projection formulas, induced representations and their characters.