Winter 25/26 - Representation Theory of Algebraic Groups I

This course provides an introduction to the theory of algebraic groups and their representations. We will study the structure and classification of linear algebraic groups over algebraically closed fields, with a focus on reductive groups and their representation theory.

Topics include: basic definitions and examples of algebraic groups, Jordan decomposition, tori and their characters, Borel subgroups and the Borel fixed point theorem, root systems and root data, structure theory of reductive groups, and an introduction to their representation theory.

• Linear Algebraic Groups, James E. Humphreys
• Linear Algebraic Groups, Armand Borel
• Introduction to Algebraic and Constructive Real Geometry, Michel Coste
• Algebraic Groups and Their Lie Algebras, Gunter Malle and Donna Testerman
• Representations of Algebraic Groups, Jens Carsten Jantzen
• Algebraic Groups, J. S. Milne

Lectures

Wednesday 10-12, Room: 04-516
Thursday 10-12, Room: 04-516

Exams

There will be an oral exam at the end of the semester. More details will be provided during the course.