INTRODUCTION TO REPRESENTATION THEORY-
Spring 2019-2020
Schedule: Monday
12:40 - 13:30, M106 , Friday 10:40 -
12:30, 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
30, Exam 1 60, Exam 2 60, Final Exam
60, Total 210
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
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 |
Chapter
3 |
Chapter
3 , # 1,2,7,8 |
|
3 |
FG-modules,
submodules, |
Chapter
4, |
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 |
Chapter
8 |
Chapter
8; #3,5 |
|
7 |
Schur's
Lemma |
Chapter
9 |
Chapter
9; # 4,5,6 |
|
8 |
Irreducible
modules and group algebra |
Chapter
10 |
Chapter
10; # 1,2,3,4,6 |
|
9 |
More
on group algebra, conjugacy classes |
Chapter
11, 12 |
Chapter
11; # 2,3,4 |
|
|
|
|
Chapter
12; # 1,2,6 |
|
10 |
Characters |
Chapter
13 |
Chapter
13, # 1,2,3, 7,8,10 |
|
11 |
Inner
product of characters |
Chapter
14 |
Chapter
14, # 1,2,3,4,7,8 |
|
12 |
Inner
products of characters, decomposition of modules, idempotent decomposition |
Chapter
14 |
Chapter
14; # 25--28 |
|
13 |
The
number of irreducible characters |
Chapter
15 |
Chapter
15; #1,2,3,4 |
|
14 |
Character
tables and orthogonality relations |
Chapter
16 |
Chapter
16; #1,2,3,4 |
|
15 |
Normal
subgroups and lifted characters |
Chapter
17 |
Chapter
17; #1,3,4,5, |
|
|
|
|
|