MAGIC075: Representation Theory of Groups

Course details

A core MAGIC course


Spring 2018
Monday, January 22nd to Friday, March 16th; Monday, April 23rd to Friday, May 4th


Live lecture hours
Recorded lecture hours
Total advised study hours


16:05 - 16:55
12:05 - 12:55


Please see the syllabus.


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


Representation Theory
Fall 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.


  • Dr Martina Balagovic

    Dr Martina Balagovic

    University of Newcastle


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.

  • Representations and Characters of Groups (G. James, M. Liebeck, book)
  • Character Theory of Finite Groups (Isaacs, book)
  • Methods of Representation Theory ( C. Curtis, I. Reiner, book)
  • Introduction to representation theory (Etingof, )
  • Linear representations of finite groups (Serre, )


The assessment for this course will be released on Monday 7th May 2018 and is due in by Monday 21st May 2018 at 23:59.

The assessment for this course will be via a single take-home paper in May with 2 weeks to complete and submit online. It should take about 3h to complete. You will need 50

Please note that you are not registered for assessment on this course.


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