Fall 2025

Representation Theory II (V4A3)

Exam. There will be written exams at the end of the semester. Seminar. There will also be a seminar on representations of SL₂. Instructors. Dr. Jonas Antor Dr. Johannes Flake Lectures.

• Tuesdays, 10 am–12 pm, Kleiner Hörsaal, Wegelerstr. 10
• Fridays, 10 am–12 pm, Zeichensaal, Wegelerstr. 10

Tutorials. in Endenicher Allee 60, Neubau, N 0.003:

• Mondays, 10 am–12 pm
• Wednesdays, 2 pm–4 pm

References.

• Etingof–Gelaki–Nikshych–Ostrik: Tensor categories.
• Humphreys: Linear Algebraic Groups.
• Springer: Linear Algebraic Groups.
• Turaev–Virelizier: Monoidal Categories and Topological Field Theory.

Prerequisites. Fundamental or good understanding of representation theory, for instance, from Foundations of Representation Theory and/or Representation Theory I. Basic familiarity with algebraic varieties (such as the ones covered Foundations of Representation Theory). Course content. The aim of this course is to discuss algebraic groups and tensor categories, and their fundamental role in representation theory. In the process, we will explore interesting connections to finite groups and Lie algebras.

• basic structure of linear algebraic groups and their representations
• connections to semisimple Lie algebras and their representations
• basic theory of tensor categories, including abelian and monoidal categories
• categories of representations of finite or algebraic groups
• Tannakian reconstruction and Deligne's theorem
• braidings, rigid objects, pivotal structures, ribbon structures
• connections to low-dimensional topology (knots) and TQFT