Unit information: Representation Theory in 2015/16

Unit name	Representation Theory
Unit code	MATHM4600
Credit points	20
Level of study	M/7
Teaching block(s)	Teaching Block 2 (weeks 13 - 24)
Unit director	Professor. Tim Dokchitser
Open unit status	Not open
Pre-requisites	MATH 21100 Linear Algebra 2; MATH 33300 Group Theory (may be taken concurrently).
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Unit aims

To develop the basic theory of linear representations of groups, especially of finite groups over the complex numbers. To develop techniques for constructing characters and character tables. To explore applications of the theory.

General Description of the Unit

After setting up the basics of the general theory of representations of groups, this unit will concentrate on representations of finite groups over the complex numbers. The theoretical properties of the character table of a group will be studied in detail, together with practical methods of calculating the character tables of particular groups, and several applications of the theory will be given.

Relation to Other Units

This is one of three Level 7 units which develop abstract algebra in various directions. The others are Galois Theory and Algebraic Topology.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

Intended Learning Outcomes

Learning Objectives

After taking this unit, students should:

• know the standard general properties of the character table of a finite group, and have an understanding of why these properties hold.
• be able to apply a variety of methods for constructing characters.
• be able to deduce properties of a group from its character table.

Transferable Skills

The application of abstract ideas to concrete calculations. The ability to tackle problems by making a sensible choice from among a variety of available techniques.

Teaching Information

Lectures, exercises to be done by the students. (If there is not sufficient demand this unit may be given as a directed reading course, or not at all).

Assessment Information

100% Examination.

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

Reading and References

• G. James and M. Liebeck, Representations and characters of groups, 2nd Edition C.U.P., 2001.

• W.Ledermann, Introduction to group characters, C.U.P., 1977.

• J.-P.Serre, Linear representations of finite groups, Springer, 1977

• C.B. Thomas, Representations of Finite and Lie Groups, Imperial College Press, 2004

James and Liebeck is the recommended book. Ledermann covers similar material, but in a little less detail. Serre is concise and elegant, and may be more useful for consolidating ideas than for a first treatment.