INTRODUCTION TO REPRESENTATION THEORY- Spring 2025
Instructor: SEMRA
ÖZTÜRK
Please
check this page often for further
announcements this week, and
come to lectures, we will start from the beginning on Tuesday, Feb 25 at 12:40.
NEW!! Updated Feb 21 at
20:00
Math 464 is very likely to survive J
Today
there were 5 students in class, they
requested to move Wednesday 12:40 lecture
to Friday 16:40.
The proposed
exam dates are : April 5, and May 10 at 10:00
1) If you are interested in the course (and satisfy the prerequisite) please add this course when the registration system is active and get approval as soon as possible. There
is no need to send me e-mail. Just add the course.
2) To
see if there are overlapping for students who interested in the course but were not in class today, I ask ALL students who will register to vote in the new short poll below for a likely new
schedule:
|
Tuesday |
12:40 |
13:30 |
M105 |
|
Friday |
15:40 |
17:30 |
M105 |
----------------------------------------------------------------------
Updated Feb
19 at 14:00
According to
the poll the schedule in the registration system should be the schedule for the course if there are no
new students next week.
Schedule :
|
Tuesday |
12:40 |
13:30 |
M105 |
|
Wednesday |
12:40 |
13:30 |
M105 |
|
Friday |
15:40 |
16:30 |
M105 |
Please attend the
lectures, we started today with two students only!
(Tuesday and Wednesday
there is no overlap, for friday there are
overlaps with two courses but I must ignore that. So the sechedule is
fixed now if all the studentswho voted in the poll register .) For all of us to know the course is not closed, you should register as
early as possible, and get the approval as soon as possible.
Update Feb 18
If
you want to add this course (and stisfy
the prerequisite) please
1)
fill in the form below for schedule arrangement
2)
come to the
lectures according to the schedule in the registration system (which is updated
on Feb 18).
3)
write an email to sozkap@metu.edu.tr if you have not done earlier stating your
interest
4)
add this course next week when the registration system
is active
Office
: M 138, sozkap@metu.edu.tr, For
my schedule see http://users.metu.edu.tr/sozkap/aa.pdf
Grading : Exam 1
60pts, Exam 2 60pts, Final Exam 60, 20 pts
attendance /hw ??
Total 200.
Policies : Lecture
attendance is required unless there is an overlapping course you are taking, in
case of 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
Tentative Weekly :
|
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, |