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This course is part of the MAGIC core.


Please see the syllabus.


Spring 2017 (Monday, January 23 to Friday, March 31)


  • Wed 11:05 - 11:55
  • Thu 12:05 - 12:55


A course on group theory and a good background in linear algebra.


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.


Kay Magaard


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Mashaer Alsaeedi
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Turki Alsuraiheed
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Stuart Bond
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Ho Yiu Chung
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Padraig Condon
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Richard Hatton
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Vijay Joshi
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Ulla Karhumäki
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Bianca Loda
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James Macpherson
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Rosario Mennuni
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William Norledge
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Andrea Pachera
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Sam Povall
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Jack Saunders
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Kathryn Spalding
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Anna Szumowicz
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Matty Van Son
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George Witty
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Yiru Ye
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Di Zhang


Representations and Characters of GroupsG. James, M. Liebeck
Character Theory of Finite GroupsIsaacs
Methods of Representation Theory C. Curtis, I. Reiner


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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 three questions worth a total of 60 marks. The pass mark is 30/60.


Files:Exam paper
Released: Monday 24 April 2017 (118.2 days ago)
Deadline: Sunday 7 May 2017 (104.2 days ago)


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Recorded Lectures

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