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This course is part of the MAGIC core.


Please see the syllabus.


Spring 2019 (Monday, January 21 to Friday, March 29)


  • Live lecture hours: 20
  • Recorded lecture hours: 0
  • Total advised study hours: 80


  • Mon 11:05 - 11:55
  • Fri 10:05 - 10:55


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


Representation Theory
Spring Term
Lecturer: Martina Balagovic

Outline of course: This course is an introduction to the representation theory of finite groups. We will develop the basic theory of finite dimensional representations over C. The main results are that such representations are completely reducible and completely determined by their characters. We will also see how characters are used to effectively calculate such decompositions. We will finish the course by studying two classes of examples.

Course Plan:
  • Review of linear algebra (complex inner product spaces, spectral theorem)
  • General linear group
  • (Complex) representations of groups
  • Maschke’s Theorem
  • Morphisms of representation, Schur’s Lemma
  • Orthogonality relations
  • Class functions, characters, and character tables
  • Regular representation
  • Representations of abelian groups
  • Representations of the symmetric group

Reference Texts:
  1. W. Fulton, J. Harris; Representation Theory - A First Course
  2. P. Etingof, O. Golberg, S. Hensel, T. Liu, A. Schwendner, D. Vaintrob, E. Yudovina; Introduction to representation theory
  3. J.-P. Serre; Linear representations of finite groups
  4. C. Curtis, I. Reiner; Methods of Representation Theory, John Wiley & Sons, New York 1981.
  5. I. M. Isaacs; Character Theory of Finite Groups, Academic Press, New York 1976.
  6. G. James, M. Liebeck; Representations and Characters of Groups, 2nd Edition, Cambridge University Press, 2001.


Martina Balagovic
Photo of Martina Balagovic
Profile: Research interests: algebra, representation theory, quantum groups, quantum affine algebras, Kac-Moody algebras, double affine Hecke algebras and their degenerations, quantum symmetric pairs, Lie superalgebras, diagram algebras


Representations and Characters of GroupsG. James, M. Liebeck
Character Theory of Finite GroupsIsaacs
Methods of Representation Theory C. Curtis, I. Reiner
Introduction to representation theoryEtingof
Linear representations of finite groupsSerre


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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 a total 6 questions, you should attempt and submit your answers to 4 questions of your choice, and you will need the equivalent of 2 questions to pass.

MAGIC075 Representation Theory of Groups Exam 2018/2019

Files:Exam paper
Released: Sunday 28 April 2019 (148.4 days ago)
Deadline: Sunday 12 May 2019 (133.4 days ago)

There are 6 questions; choose 4 questions to answer, and write clearly which questions you have chosen. Each question carries 25 marks. The pass mark is 50/100. Prove all your claims.

Recorded Lectures

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