INTRODUCTION TO
REPRESENTATION THEORY- Spring 2021-2022
Schedule: Monday
12:40 - 13:30, M106 , Thursday 13:40 -
15:30, M106
Instructor: SEMRA
ÖZTÜRK
Office
: M 138, sozkap@metu.edu.tr, For
my schedule see http://users.metu.edu.tr/sozkap/aa.pdf
Course Grading : Homework and
attendance 20, Exam 1 25, Exam 2 25, Final
Exam 30, Total 100
Course Policies : Class Attendance
Attendance is administered, encouraged. Class Participation
Encouraged. Late Submission of Assignments Is not recommended.
Course 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 .
Course Learning
Outcomes: Student, who passed the course
satisfactorily will be able to: construct modules over group algebra,s
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 outline
including homeworks:
|
Week |
Topic |
Relevant
Reading |
Assignments |
|
1 |
Introduction,
review of some topics: Groups, Linear transformations. |
Chapter
1, and 2 |
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 |
Holiday
week |
|
|
|
10 |
Inner
product of characters |
Chapter
14 |
Chapter
14, # 1,2,3,4,7,8 |
|
11 |
Inner
products of characters, decomposition of modules, idempotent decomposition |
Chapter
14 |
Chapter
14; # 25--28 |
|
12 |
The
number of irreducible characters |
Chapter
15 |
Chapter
15; #1,2,3,4 |
|
13 |
Character
tables and orthogonality relations |
Chapter
16 |
Chapter
16; #1,2,3,4 |
|
14 |
Normal
subgroups and lifted characters |
Chapter
17 |
Chapter
17; #1,3,4,5, |
|
15 |
Some
elementary character tables |
Chapter 18 |