Introduction to Representation Theory I
Prerequisites
Prerequisites: basic knowledge of linear algebra.
Programme
• Linear representations of finite groups: definition and first properties
• Operations on representations: direct sums, tensor products, exterior powers
• Caracters of complex representations, orthogonality relations
• Character tables of finite groups
• Induced representations, Frobenius reciprocity
• Real representations of finite groups
• A brief survey on representations of compact matrix groups
• Representations of S^1, SU_2, U_2
Educational aims
Introducing to the representation theory of finite and compact groups
Bibliographical references
J.P. Serre, Linear representations of finite groups