Coxeter groups and Lie algebras — WS 2020/21

Time
Tuesday and Thursday, 14:15 – 15:45
Place
Virtual, on BBB. Room 3414 "Spassky".
Lecturer
Johan Commelin
More info
See below for a description and literature.

Exercises

All exercises are collected in one file (with 1 section per week): exercises.pdf

Lectures

W01 Tue | W01 Thu | W02 Tue | W02 Thu | W03 Tue | W03 Thu | W04 Tue | W04 Thu

Week 1 (Tuesday)

Week 1 (Thursday)

Week 2 (Tuesday)

Week 2 (Thursday)

Week 3 (Tuesday)

This week we take a step back. In the last two weeks, the pace was very high. My apologies for that. From now on, the pace should be slower. We will see a bit of new content this week, but it would also be good to use the extra time to review material from last week. On Tuesday, we look at the Jordan decomposition. Next time (Thurday), we will look at multilinear algebra: tensor products, symmetric powers, alternating powers.

Week 3 (Thursday)

Week 4 (Tuesday)

Week 4 (Thursday)

Description

Coxeter groups and Lie algebras are central notions in so-called Lie theory. They appear naturally in the study of representation theory of (certain) infinite groups, and have applications in various other fields of mathematics such as differential geometry, algebraic geometry and number theory. In this course we will learn about the basic properties of Coxeter groups and reflection groups, root systems, and Lie algebras. We will see how these concepts interact with each other, and finally learn about the marvellous classification in terms of Dynkin diagrams: a certain type of decorated graphs that naturally fall apart into four infinite lists and a handful of ``exceptional'' examples.

Literature