Representation Theory IV 0.5 Group theory 1.1 Definitions and first examples

1 Representation theory of finite groups

Throughout, unless specified otherwise, $G$ denotes a finite group and $V$ denotes a finite dimensional complex vector space (such as $\mathbb{C}^{n}$ ).

1.1 Definitions and first examples

1.2 Formalities

1.3 Example: dihedral groups

1.4 Schur’s Lemma

1.5 Maschke’s theorem and complete reducibility

1.6 The group ring and the regular representation