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 19972000 Tripos
ps
pdf
Version 1.0 (May 3, 2001)
Free Stuff on the Web
- T.Y. Lam's expository article: Representations of Finite Groups:
A Hundred Years
- 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
- 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)
- 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