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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

Lecturer


Kay Magaard
Email k.magaard@bham.ac.uk
Phone
vcard


Students


Photo of Bander Almutairi
Bander Almutairi
(East Anglia)
Photo of Stacey Aston
Stacey Aston
(Newcastle)
Photo of Daniel Buck
Daniel Buck
(East Anglia)
Photo of Zhen Cui
Zhen Cui
(Exeter)
Photo of Betty Fyn-Sydney
Betty Fyn-Sydney
(Birmingham)
Photo of Tom Harris
Tom Harris
(Southampton)
Photo of Robert Henderson
Robert Henderson
(East Anglia)
Photo of Heather Johnson
Heather Johnson
(Lancaster)
Photo of Alexandrou Maria
Alexandrou Maria
(Manchester)
Photo of Linyu Peng
Linyu Peng
(Surrey)
Photo of Jeevan Rai
Jeevan Rai
(Surrey)
Photo of Amin Saied
Amin Saied
(Southampton)
Photo of David Ward
David Ward
(Manchester)
Photo of Magdalena Zajaczkowska
Magdalena Zajaczkowska
(Loughborough)


Prerequisites


No prerequisites information is available yet.

Syllabus


Representation Theory
Fall Term
Lecturer: Kay Magaard
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:
  1. C. Curtis, I. Reiner; Methods of Representation Theory, John Wiley & Sons, New York 1981.
  2. I. M. Isaacs; Character Theory of Finite Groups, Academic Press, New York 1976.
  3. 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
Note:

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 (994.2 days ago)


Task 2

Deadline: Thursday 15 December 2011 (980.2 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