INTRODUCTION TO REPRESENTATION THEORY- Spring 2026
Instructor: SEMRA
ÖZTÜRK
Office
: M 138, sozkap@metu.edu.tr, For
my schedule see http://users.metu.edu.tr/sozkap/aa.pdf
Grading : Updated Feb
13, 2026
Mid Term Exam 40 pts
April 18, at 12:00, Final Exam 40 pts, 10 pts attendance, 10
pts hw ; Total 100.
Policies : Lecture
attendance is required unless there is an overlapping course you are taking, in
case of (verified) course overlaps this will not be a problem.
Objectives: At the
end of this course, the student will learn: basic concepts used in
representation theory, such as modules,
decomposing modules into irreducibles, computing character
tables, obtaining information about the group from the character
table of the group .
Learning Outcomes: Student,
who passed the course satisfactorily will be able to: construct modules over
group algebras, determine the type of the group algebra, deteremine
irreducibility of a given module compute the character table of a
group, derive information about the group from its character table.
Text book : Representations and Characters of Groups, by G. James and M. Liebeck, Cambridge University
Press
Useful Sources
1.
Algebras and Representation Theory By Erdmann and
Holmsen https://link.springer.com/content/pdf/10.1007/978-3-319-91998-0.pdf
2.
Rings Modules and Linear algebra by Strickland modules.pdf
Tentative Syllabus including
suggested problems from the Textbook:
|
Week |
Topic |
Relevant
Reading |
Suggested
problems |
|
1 |
Introduction,
review of some topics: Groups, subgroup lattices, linear transformations |
Chapter
1, |
Chapter
1, # 2,
4,7,10 Chapter
2, # 5 (b), 7,9 |
|
2 |
Group
Representations, FG-modules |
Chapter
3, and 4 |
Chapter
3, # 1,2,7,8 |
|
3 |
Submodules,
permutation modules |
Chapter
4, and 5 |
Chapter
4, # 2,3,4. |
|
4 |
FG-modules
and irreducibility |
Chapter
5 |
Chapter
5, # 1,3 |
|
5 |
Group
algebras and FG-homomorphisms |
Chapter
6, 7 |
Chapter
6, # 1, 4, Chapter
7, # 1, 3 |
|
6 |
Maschke's Theorem, Schur's
Lemma |
Chapter
8, and 9 |
Chapter
8, # 3,5, Chapter
9, # 4,5,6 |
|
7 |
Irreducible
modules and group algebra |
Chapter
10, and 11 |
Chapter
10, # 1,2,3,4,6 |
|
8 |
More
on group algebra, conjugacy classes, Characters |
Chapter
11, 12, 13 |
Chapter
13, # 1,2,3, 7,8,10 |
|
9 |
Inner
product of characters |
Chapter
14 |
Chapter
14, # 1,2,3,4,7,8 |
|
10 |
Inner
products of characters, decomposition of modules, idempotent decomposition |
Chapter
14 |
Chapter
14, # 25--28 |
|
11 |
The
number of irreducible characters |
Chapter
15 |
Chapter
15, #1,2,3,4 |
|
12 |
Character
tables and orthogonality relations |
Chapter
16 |
Chapter
16, #1,2,3,4 |
|
13-15 |
Some
elementary character table, Normal subgroups and
lifted characters |
Chapter 18,
17 |
Chapter
17, #1,3,4,5, |