Winter 2021/22 - V4A5 Advanced Algebra I
(Introduction to canonical bases and crystals)



Announcements:
The exam will be oral. It will take place the first week after the lectures end (Thus, the exam will be in the week of February 7–11). Details will be announced in the lectures.
Old Announcement: Note that Exercise Sheet #9 is due on Monday, January 10.

Lectures:
Wednesdays 10–12 in the Zeichensaal on Wegelerstrasse 10, and
Fridays 10–12 in Room 1.008 of the MI.
The first lecture is on October 13.
The lecture course will be held online on Zoom: the login information can be found on Basis.

Instructor: Prof. Dr. Catharina Stroppel
Assistant: Dr. Jacob Matherne

Course content: The lectures will give an introduction to canonical bases and crystals. We will provide the necessary knowledge and facts on quantum groups and their representation theory.

Prerequisites for the course: Good knowledge of Lie theory is required and knowledge of quantum groups is helpful. In particular, we assume the book "Introduction to Lie algebras and representation theory" by J. Humphreys (zbMATH Open link).

Exercise sessions (Tutorials): Wednesdays 18–20
The first exercise session is on October 20.
The exercise sessions will be held in person in MI SemR 1.008.

Some references:

  1. J. Hong and S.-J. Kang - Introduction to quantum groups and crystal bases (zbMATH Open link)
  2. J. Jantzen - Lectures on quantum groups (zbMATH Open link)
  3. V. Chari and A. Pressley - A guide to quantum groups (zbMATH Open link)
  4. C. Kassel - Quantum groups (zbMATH Open link)
  5. G. Lusztig - Introduction to quantum groups (zbMATH Open link)
  6. R. Carter - Lie algebras of finite and affine type (zbMATH Open link)
  7. V. G. Kac - Infinite dimensional Lie algebras (zbMATH Open link)