Representations of Classical Groups
Lecture Course in the Summer Semester 2024
This course offers a first introduction to (classical) Lie groups, Lie algebras and their representations.
This is a very elegant theory with ubiquitous applications throughout mathematics, but also theoretical physics - which will be one of our inspirations and source of examples.
Info
Join the Müsli & the MaMpf page of course!
Description
Instructor
Lecturer: Dr. Simone Noja, Email
TAs: S. Schmidt Email & R. Senghaas Email
Time and place
Lectures on Tuesday & Thursday, 16-18, in Mathematikon SR B. First class on April 16
Prerequisites
Linear algebra is a basic prerequisite. A basic understanding of differential geometry of manifolds might help, but it is not required.
Structure & Exam
The course will consist in front lectures, where the theory and its applications will be discussed. During the course, there will be three (separared) weeks of 'break' from ordinary lectures, with focus on exercises.
The course is settled via in-class exam. The student will be asked to discuss some theoretical topics, and solve some exercises.
Bibliography
The notes of the classes will be made available on MaMf. A not-at-all exhaustive list of useful references of the topics covered is given below.
- J. Fuchs, C. Schweigert, Symmetries, Lie Algebras and Representations, CUP (1997)
- W. Fulton, J. Harris, Representation Theory, Springer (2004)
- B.C. Hall, Lie Groups, Lie Algebras, and Representations, Springer (2003)
- J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer (1972)
- A. Knapp, Lie Groups Beyond and Introduction, Birkhäuser (2004)
- V.S. Varadarajan, Lie Groups, Lie Algebras, and their Representations, Springer (1984)
