MAGIC075: Representation Theory of Groups

Course details

A core MAGIC course


Spring 2020
Monday, January 20th to Friday, March 27th


Live lecture hours
Recorded lecture hours
Total advised study hours


11:05 - 11:55 (UK)
10:05 - 10:55 (UK)


Please see the syllabus.


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

Related courses


Representation Theory 
 Spring Term
Lecturer: Martina Balagovic 

Outline of the course: This course is an introduction to the representation theory of finite groups. We will develop the theory of finite dimensional representations of finite groups over the field of complex numbers. The main results are that such representations are completely reducible, that there are finitely many irreducible representations, and that such representations are completely determined by their characters. We will also see how characters are used to effectively calculate such decompositions. We will finish the course by looking at induction and restriction functors which let us move between the categories of representations of different groups, looking briefly at what happens over other fields, and considering representations of the symmetric group. 

 Course Plan:

  • Introduction, definitions and main questions
  • Review of linear algebra (complex inner product spaces, spectral theorem) 
  • Maschke's Theorem 
  • Schur's Lemma 
  • Representations of abelian groups
  • Examples (symmetric, dihedral groups)
  • The group algebra and the regular representation
  • Characters
  • Induction, coinduction, restriction
  • Other fields
  • 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


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  • 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 20th April 2020 at 00:00 and is due in before Monday 4th May 2020 at 11:00.

The assessment for this course will be via a single take-home paper in the Spring. You will need to answer 4 questions (5 or 6 might be offered), each carrying 25 marks, and you will need 50 marks to pass. 

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


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