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Representations of compact groups [MA5054]

Sommersemester 2021

Lecturer: Prof. Dr. Robert König
Assistants: Farzin Salek, Zahra Khanian
Lecture: Thursdays 4:15pm – 5:45pm (zoom)
Exercises: Fridays 4:00pm - 5:30pm (zoom)

News

There will be no lecture on May 13 (holiday). The exercises on Friday the 14th will take place as usual.

Contents

This course will serve as an introduction to the theory of Lie groups and their representations, a topic of central importance in physics. Subjects to be covered include:

In addition, some applications to physics may be discussed.

Exercises

Exercises Solutions Topics To be discussed on
Assignment 1 Solution 1 Manifolds and groups April 23
Assignment 2 Solution 2 Tangent vectors and push-forwards April 30
Assignment 3 Solution 3 Vector fields May 7
Assignment 4 Solution 4 Exponential map and Lie algebra May 14
Assignment 5 Solution 5 Connected abelian lie groups May 21

Literature

There are plenty of excellent textbooks on these topics. The lectures will follow the second half of

to a large extent. Other recommended literature (more may be provided during the course):

Some notes

Continuously updated (partial) lecture notes/summary.

Files Lecture
Review topological/smooth manifolds Lecture 1
Motivation (Laplace-Operator), Tangent space, differential maps Lecture 2
Vectorfields, integral curves, derivations, left-invariance Lecture 3
One-parameter groups, Lie algebra, Ad-map and differential Lecture 4