Representation Theory of the Symmetric Group
The aim of the module is to introduce students to the modern representation theory by working with the classical example, the group of all permutations of a finite set.
At 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.
- Conjugacy classes in the symmetric group and combinatorics of Young diagrams.
- Robinson-Schensted-Knuth algorithm.
- General properties of representations of finite groups.
- General properties of characters of finite groups.
- Young symmetrizers and the regular representation of the symmetric group.
- Hook formula for the dimensions of irreducible representations of the symmetric group.
- G D James, The representation theory of the symmetric group, Lecture Notes in Mathematics #682, Springer, 1978 (S 0.4 LEC).
- I G Macdonald, Symmetric functions and Hall polynomials, Oxford University Press, 1979 (S 2.86 MCD).
- B E Sagan, The symmetric roup: representations, combinatorial algorithms and symmetric functions, Wadsworth and Brooks/Cole, 1991 (S 2.86 SAG).
- Autumn Term
- 2 lectures per week
- problems classes by request
- Examination in week 1 Spring Term (90%),
- Coursework (10%). Note that coursework submitted after the advertised deadlines will be given a mark of zero.
This module is not available as an elective.
Back to the Top