MAGIC075: Representation Theory of Groups

Course details

A core MAGIC course

Semester

Spring 2014
Monday, January 20th to Friday, March 28th

Hours

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

Timetable

Wednesdays
13:05 - 13:55
Thursdays
11:05 - 11:55

Description

Please see the syllabus.

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 Characters, Frobenius reciprocity, permutation characters.
  • (Weeks 8 and 9) Clifford's theorem and consequences.
  • (Weeks 9 and 10) Forbenius' theorem and related results.

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

Description

The assessment for this course will be via a single take-home paper in April with 2 weeks to complete and submit online. There will be 3 questions and you will need to the equivalent of 3/2 questions to pass

Assessment not available

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Files

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Lectures

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