Group Representation Theory (0540505) 10 credits

Representation Theory of the Symmetric Group

This is the version for the year beginning on 1 September of the year

Please note that our courses change slightly from year to year and check that you are looking at the version for the right year. If necessary, click as appropriate for the version for

• this year (i.e. from 1 September last to 31 August next)
• next year
• last year.

Aims

To introduce students to the modern representation theory by working with the classical example, the group of all permutations of a finite set.

Learning Objectives

By the end of the module students should know:

• classical combinatorics related to the symmetric group,
• general properties of representations and characters of finite groups,
• explicit construction of irreducible representations of the symmetric group.

• Matrices, Linear Algebra, Geometry (0500007)
• Introduction to Group Theory (0500011)
• Linear Algebra (0590014)

1. Conjugacy classes in the symmetric group and combinatorics of Young diagrams.
2. Robinson-Schensted-Knuth algorithm.
3. General properties of representations of finite groups.
4. General properties of characters of finite groups.
5. Young symmetrizers and the regular representation of the symmetric group.
6. Hook formula for the dimensions of irreducible representations of the symmetric group.

1. G D James, The representation theory of the symmetric group, Lecture Notes in Mathematics #682, Springer-Verlag, 1978 (NORTH ROOM QUARTO S 0.4 LEC) *
2. I G Macdonald, Symmetric functions and Hall polynomials, Oxford University Press, 1979 (S 2.86 MCD) *
3. B E Sagan, The symmetric roup: representations, combinatorial algorithms and symmetric functions, Wadsworth and Brooks/Cole, 1991 (S 2.86 SAG) *

• 2 lectures per week
• problems solving session by request

Term taught

Autumn

Assessment

• 1½ hour unseen examination in week 1 Spring Term (90%)
• Coursework (10%)

Elective information

Not available

Return to list of fourth year modules

Return to list of modules in this dept available to students from other depts

Return to Mathematics home page

Revised 1 September 2003