###
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

- 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