Representation Theory

Content

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Description

Time: Mondays, 13,00 - 15.00

Location for Maxwell Institute students: Bayes Centre (room 5.46)

Module Leader: TBC

Module Summary

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).

Assessment

This module is assessed in two equally weighted assignments, each worth 50% of the Final Grade.