MMA201 H19 Representationsteori

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This page contains the program of the course: lectures, exercise sessions and computer labs. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

The preliminary lecture notes are here (last updated 17 October)

lectures-new-5.pdf

A checklist for the course contents

theory.pdf

Here are two old exams for the very similar course MMA200

171026-1.pdf

180822.pdf

Here is the exam 191101 with solutions

191101.pdf

 

Program

The schedule of the course is in TimeEdit.

Normally we will have exercise classes on Monday and lectures on Tuesday and Thursday.

Note that there is no lecture Thursday 3 October and Thursday 10 October. These have been moved to Wednesday 2 October and 9 October 10:00-11:45.

Rough plan

Week Chapter Contents
2-6/9 1-2 Review of group and ring theory
9-13/9 3, 4 Modules, tensor algebra
16-20/9 5 Modules over a PID
23-27/9 5 Canonical forms
30/9-4/10 6 Group representations
7-11/10 6 Group representations
14-18/10 7 Representations of the symmetric group
21-25/10 8 Representations of compact groups?

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Detailed plan

Day Chapter Contents/Exercises
2/9 1.1-1.4 Review of group theory
3/9 1.5-2.2 Review of ring theory
5/9 2.3 Unique factorization domains
9/9

1.2.4, 1.5.3, 1.7.4, 1.7.5, 1.7.15, 1.7.17, 2.2.4, 2.4.6, 2.4.7, 2.4.8
10/9 3

Modules
12/9 4.1-4.2

Tensor products
16/9

3.2.2, 3.5.2, 3.5.3, 3.5.5, 3.7.6, 3.7.8, 4.1.1, 4.2.3, 4.4.1, 4.4.2
17/9 4.3, 5.1

Symmetric and antisymmetric tensors

Introduction to modules over PID
19/9 5.2

Classification of modules over PID
23/9

4.3.2, 4.3.3, 4.3.5, 4.4.1, 4.4.2, 4.4.3, 5.1.1, 5.2.1, 5.2.2, 5.2.3
24/9 5.3-5.5

Canonical forms
26/9 6.1

Group representations
30/9

5.4.1, 5.4.2, 5.6.1, 5.6.4, 5.6.5, 5.6.6, 6.1.1, 6.1.5
1/10 6.2-6.3

Characters
2/10 6.4-6.6, 6.9

The character table, Frobenius divisibility
7/10

6.2.1, 6.4.1, 6.5.2, 6.5.3, 6.6.1, 6.9.2, 6.9.4, 6.10.2, 6.10.3
8/10 6.7-6.8

Fourier transform on finite groups
9/10 7.1-7.2

Representations of the symmetric group
14/10 7.3

Explicit realizations of representations
15/10 7.4-7.6

Schur-Weyl duality, Characters
17/10

6.7.2, 6.7.5, 6.9.4, 7.1.1, 7.1.3, 7.2.5, 7.3.1, 7.3.2, 7.3.3, 7.4.1
21/10 7.6-7.7

Characters
22/10 8

Compact groups, SU(2)
24/10

Course evaluation, repetition

Look at the two old exams posted above

 

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Course summary:

Date Details Due