Summer 24 - V5A5 - Advanced Topics in Representation Theory - Kac-Moody Algebras and Flag Varieties

This is the course website for the lecture course Advanced Topics in Representation Theory in Summer 2024.


Kac-Moody algebras and groups are (mostly infinite-dimensional) generalisations of semisimple Lie algebras and groups. We recall the classification and Serre relations of semisimple Lie algebras via their root system as well as their Verma modules and highest weight representations. We then define Kac-Moody Lie algebras via their generalised Cartan matrix and discuss their structure and representation theory in analogy to the semisimple Lie algebras. Lastly, we will discuss the construction of Kac-Moody groups and flag varieties. We will discuss the geometry of their Schubert varieties, with a focus on the affine Grassmannian.


Lecture Notes

Preliminary lecture notes will be found here.


Some sources that the course is based on:



There are two lectures per week:

Wednesday 12-14, Room: Endenicher Allee 60, Seminarraum 1.008,
Friday 10-12, Room: Endenicher Allee 60, Seminarraum 0.006.


There will be exercise problems posed in the lectures.


There will be an oral exam on Friday, the 26th of July. More information on the time will follow.