General
This course is part of the MAGIC core.
Description
Please see the syllabus.
Semester
Autumn 2011 (Monday, October 10 to Friday, December 16)
Timetable- Wed 12:05 - 12:55
- Thu 12:05 - 12:55
Students
|
Bander Almutairi
(East Anglia) |
Stacey Aston
(Newcastle) |
Daniel Buck
(East Anglia) |
Thomas Bullock
(York) |
|
Zhen Cui
(Exeter) |
Betty Fyn-Sydney
(Birmingham) |
Oliver Goodbourn
(York) |
Thomas Harris
(Southampton) |
|
Robert Henderson
(East Anglia) |
Heather Johnson
(Lancaster) |
Alexandrou Maria
(Manchester) |
Linyu Peng
(Surrey) |
|
Jeevan Rai
(Surrey) |
Amin Saied
(Southampton) |
David Ward
(Manchester) |
Magdalena Zajaczkowska
(Loughborough) |
Prerequisites
No prerequisites information is available yet.
Syllabus
Fall Term
Outline of course: This course is an introduction to the representation theory of finite groups. We will develop the basic theory of ordinary representations and their characters. Along the way we will compute the charcter tables of particular classes of groups. We will also examine how structural information of a group can be obtained from its character table. For large parts we will mostly follow Isaacs book; see the references below.
Course Plan:
- (Week 1) Basic definitions, the group algebra, Wedderburn theory.
- (Week 2) Characters and the Orthogonality relations.
- (Week 3) Examples of character tables.
- (Week 4) Integrality, Burnside's paqb Theorem.
- (Weeks 5) Products of characters, the representations ring.
- (Week 6) Involutions and the Brauer-Fowler Thereom
- (Week 7) Induced Charaters, Frobenius reciprocity, permutation characters.
- (Week 8) Clifford's theorem and consequences.
- (Week 9) Forbenius' theorem and related results.
- (Week 10) Representation theory of symmetric groups.
Reference Texts:
- C. Curtis, I. Reiner; Methods of Representation Theory, John Wiley & Sons, New York 1981.
- I. M. Isaacs; Character Theory of Finite Groups, Academic Press, New York 1976.
- G. James, M. Liebeck; Representations and Characters of Groups, 2nd Edition, Cambridge University Press, 2001.
Bibliography
| Representations and Characters of Groups | G. James, M. Liebeck |
| Character Theory of Finite Groups | Isaacs |
| Methods of Representation Theory | C. Curtis, I. Reiner |
Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.)
Assessment
Two tasks containing a total of 20 problems worth 5 points each.
The first task is due on December 1 and the second on December 15, 2011.
To pass a total of 50 points is required.
Assignments
Task 1
| Deadline: | Thursday 1 December 2011 (539.9 days ago) | ||
Task 2
| Deadline: | Thursday 15 December 2011 (525.9 days ago) | ||
Files
Files marked L are intended to be displayed on the main screen during lectures.
| Week(s) | File | |
|---|---|---|
| Handout4.pdf | ||
| Task1.pdf | ||
| Task2.pdf |