Part IIB of the Mathematical Tripos:

B2. Representation Theory

Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Lent 2001

24 lectures

The aim of this course is to introduce both pure and applied mathematicians to the representation of finite groups in groups of matrices. In the latter part of the course 'finite' is replaced by 'compact', leading to more general results with very little extra effort. The Part IB course Groups, Rings and Fields is very useful and Functional Analysis is useful.

Lecturer: Ian Grojnowski
B0.28, Centre for Mathematical Sciences, Wilberforce Road, Cambridge
E-mail: I.Grojnowski@dpmms.cam.ac.uk
Tel: 37930

Supervisor: Lek-Heng Lim
D0.11, Centre for Mathematical Sciences, Wilberforce Road, Cambridge
E-mail: L.H.Lim@dpmms.cam.ac.uk
Tel: 37922

Solutions to the Example Sheets

[added June 4, 2005: solutions removed at current course instructor's request]

Example Sheet 1 ps pdf
Version 1.1 (March 16, 2001)

Example Sheet 2 ps pdf
Version 0.3 (March 16, 2001)

Example Sheet 3 ps pdf
Version 0.2 (June 1, 2001)

Example Sheet 4 ps pdf
(Coming Easter)

Extra Materials

A Few Words on Induced Representations ps pdf
Version 1.1 (March 10, 2001)

Problems on Representation Theory from the 1997–2000 Tripos ps pdf
Version 1.0 (May 3, 2001)

Free Stuff on the Web

ATLAS of Finite Group Representations

Bob Howlett's course notes on Group Representation Theory

T.Y. Lam's expository article: Representations of Finite Groups: A Hundred Years
- Part I ps pdf
- Part II ps pdf

Ron Solomon's expository article: On Finite Simple Groups and Their Classification ps pdf

H. Hoehnke and K.W. Johnson, The 1-, 2-, and 3-Characters Determine a Group pdf

Larry Smith, Polynomial Invariants of Finite Groups. A Survey of Recent Developments dvi ps pdf

Anthony Knapp's
- expository article: Group Representations and Harmonic Analysis from Euler to Langlands
  - Part I ps pdf
  - Part II ps pdf
- PCMI lecture notes: Representations of Semisimple Lie Groups dvi ps pdf

James Arthur's expository article: Harmonic Analysis and Group Representations ps pdf

Dan Barbasch's lecture notes:
- Lie Algebras ps
- Representations of Real and p-adic Groups ps
  (the first few pages contain a brief overview of induced representations and compact groups)

David Vogan's
- Notes on Representations of SL(2,R) dvi ps
- other expository papers

Brian Boe's List of Representation Theorists

Some book reviews
- Bertram Huppert, Character Theory of Finite Groups, de Gruyter, Berlin, 1998 (Reviewed by I.M. Isaacs) dvi ps pdf
- William Fulton, Young Tableaux: With Applications to Representation Theory and Geometry, Cambridge Univ. Press, New York, 1997 (Reviewed by Arun Ram) dvi ps pdf