MMA201 Autumn 23 Representation Theory

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This page will contain the program of the course. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

 

Program

The schedule of the course is in TimeEdit.

Except for the first week we will have exercise classes on Monday and lectures on Tuesday and Thursday. At the exercise classes, students will present and discuss solutions that they have prepared before the class.

 

Rough plan

 

Week Chapter Contents
28/8-1/9 1-3 Review of group and ring theory; Modules
4-8/9 4 Tensor products
11-15/9 5 Modules over a PID
18-22/9 5 Canonical forms
25-29/9 6 Group representations
2-6/10 6 Group representations
9-13/10 7 Representations of the symmetric group
16-20/10 8 Representations of compact groups

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Detailed plan

Day Chapter Contents/Exercises
28/8 1 Review of group theory
29/8 2

Review of ring theory
Unique factorization
31/8 3 Modules
4/9 Exercise session 1.
1.2.4, 1.7.4, 1.7.5, 1.7.19, 1.7.21, 2.1.4, 2.2.6, 2.3.7, 2.4.7, 2.4.8
5/9

4.1-4.2

 Tensor product of modules
7/9 4.3

Antisymmetric and symmetric tensor product
11/9 3.2.1, 3.2.2, 3.5.2, 3.5.3, 3.5.5
4.2.3, 4.3.2, 4.4.1, 4.4.2, 4.4.12
12/9 5.1-5.2 Finitely generated modules over a PID
14/9 5.2-5.3 Finitely generated modules over a PID, continued
18/9 3.7.6, 3.7.7, 4.4.4, 4.4.6, 4.4.9
5.1.1, 5.2.2, 5.2.3, 5.2.4, 5.3.1
19/9 5.4

Canonical forms of matrices

(5.5 is for orientation and will not be on exam)
21/9 6.1-6.2 Introduction to group representations
25/9 5.4.1, 5.4.2, 5.6.1, 5.6.2, 5.6.4, 5.6.6, 5.6.7, 6.1.1, 6.1.5
26/9 6.3-6.5 The regular representation, the character table
28/9 6.6-6.8 More on the character table, Fourier transform
2/10 6.2.1, 6.5.1,  6.6.2, 6.7.1, 6.8.2,  6.10.1, 6.10.8, 6.10.10
3/10 6.8, continued More on Fourier transform, Peter-Weyl theorem
5/10 6.9
7.1		 Frobenius divisibility
Introduction to representations of the symmetric group
9/10 6.2.3, 6.8.1, 6.8.6, 6.9.2, 6.9.4, 6.9.5, 6.10.3, 6.10.6
10/10 7.2-7.3 Irreducible representations of the symmetric group
12/10 7.4-7.5 Young symmetrizers and Schur-Weyl duality
16/10 7.6-7.8 Characters of the symmetric group
17/10 7.2.3, 7.2.5, 7.2.7, 7.3.2, 7.3.4, 7.7.1, 7.8.1, 7.10.5
19/10

Course evaluation

Repetition

 

Old exams with solutions

191101.pdf

200103.pdf

200820.pdf (distance exam because of the pandemic)

211029.pdf 

220103.pdf 

231027.pdf

Theory checklist

This list is now updated

theory-1.pdf

Course summary:

Course Summary
Date Details Due