This is the course website for the lecture course Representation Theory II in Winter 2023/24.
We study the geometry of some spaces that play an important role in the (geometric) representation theory of complex reductive groups and Lie algebras.
The course starts with a refresher on the classification, structure and representation theory of complex reductive algebraic groups. We then discuss the geometry of flag varieties and related spaces, with a special attention to the singularities of Schubert varieties. We will see how these notions generalise to Kac-Moody groups and study affine Grassmannians.
Moreover, we discuss conjugacy classes in reductive groups and the Grothendieck—Springer resolution.
If time permits, a crash course on quotient stacks will allow us to discuss the horocycle correspondence.
Wednesday 10-12, Room: Großer Hörsaal,
Friday 12-14, Room: Zeichensaal.
Wednesday 14-16, Room: 0.006.
There will be exercise problems posed in the lectures.
Everyone is encouraged to present their solutions on the blackboard during the problem session. You should do this at least once.
There will be an oral exam at the end of the semester. More information on the dates will follow.
The BASIS entry for the lecture and problem session.