Representation Theory

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Description

Overview

The course introduces the basics of representation theory of finite groups and algebras, for example: group/matrix algebras, representations and modules, their direct sums and tensor products, Maschke's theorem and character theory. We will mostly focus on the representations of the symmetric group and the general linear group. We cover Young diagrams and Schur-Weyl duality. We will end with an outlook on more advanced aspects of representation theory (e.g. representations of the Artin braid group, Hecke algebras, quantum groups and quantum Schur-Weyl duality).