Groups and representations

Spring semester 2003

Period: 03-02-2003 - 30-05-2003
(Spring vacation: 03-03-2003 - 07-03-2003)
(May vacation: 29-04-2003 - 05-05-2003)

Lectures: Monday, 13:30 - 15:30, CK N6 (N4009)

Tutor hour/
computer practice:
Wednesday, 13:30 - 15:30, CK N6 (N4009)


Topics of this course

  1. Modules and representations
  2. Semisimple rings
  3. Characters
  4. Induced representations

Syllabus

A syllabus will be made available here in weekly portions.

Modules and representations (Version of February 21, 2003)
Semisimple rings (Version of March 18, 2003)
Characters (Version of April 13, 2003)
Induced representations (Version of June 2, 2003)

The complete (and partially updated) syllabus of the course can be found here.

Exercises

The syllabus contains several exercises on different levels of difficulty. It is warmly recommended to work on these exercises.
Every week a compulsory set of exercises has to be handed in. These exercises will be made available here after monday's lecture and are due until the lecture of the following week. They can be handed in at my office (N2024) or during the lecture.

Exercises 1 February 10, 2003
Exercises 2 February 17, 2003
Exercises 3 February 24, 2003
Exercises 4 March 10, 2003
Exercises 5 March 17, 2003
Exercises 6 March 24, 2003
Exercises 7 March 31, 2003
Exercises 8 April 7, 2003
Exercises 9 April 14, 2003
Exercises 10 May 12, 2003
Exercises 11 May 19, 2003
Exercises 12 May 26, 2003

Tutor hour

The tutor hour gives opportunity to pose questions on the material presented in the lectures, to fill in details left out during the course and to look at explicit examples.
Every student is strongly encouraged to present solutions of one of the exercises every once in a while during the tutor hours.

Computer practice

Since this course puts emphasis on the algorithmic aspects of representation theory, we will use the computer algebra package MAGMA to work on explicit examples.
A number of algorithmic projects will be formulated which require to write small MAGMA programs yourselves.
Some examples for the usage of MAGMA can be found here.

Project 1 March 19, 2003: MeatAxe
Project 2 May 21, 2003: Permutation characters