MAGIC075: Representation Theory of Groups

Course details

A core MAGIC course

Semester

Spring 2011
Monday, January 31st to Friday, April 1st; Tuesday, May 3rd to Tuesday, May 3rd

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
0

Timetable

Wednesdays
12:05 - 12:55
Wednesdays
13:05 - 13:55

Description

Please see the syllabus.

Prerequisites

No prerequisites information is available yet.

Syllabus

Representation Theory
Winter 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.

Lecturer

Bibliography

Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and 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.

  • Character Theory of Finite Groups (Isaacs, book)
  • Methods of Representation Theory ( C. Curtis, I. Reiner, book)
  • Representations and Characters of Groups (G. James, M. Liebeck, book)

Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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