Representation Theory


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The first part of the course introduces the theory of representations of finite groups. We start off with the definition of an algebra, group/matrix algebra, representation/module before proving Schur's lemma. We continue with tensor products, Maschke's theorem and (lots of examples of) characters.


The second part of the course is about representations of the symmetric group and the general linear group. We cover Young diagrams and Schur-Weyl duality, and end with an outlook on more advanced aspects of representation theory.