Project IV 2021/2022
Representations of symmetric groups
Supervisor: Jack Shotton
Description
Representation theory is about classifying all the ways that a group can act on a vector space, and is a central topic in modern mathematics. The symmetric groups provide a rich class of examples. We will see that the irreducible representations of Sn are parametrised by partitions, which are ways of writing n as a sum of (unordered) positive integers. This opens the door to lots of beautiful connections between algebra and combinatorics, some of which we will explore in this project.
Prerequisites:
Algebra II
Corequisites:
Representation Theory IV
Textbooks:
- Bruce Sagan, The symmetric group: representations, combinatorial algorithms, and symmetric functions, Springer 1991
- Gordon James, The representation theory of symmetric groups, Springer 1978
- Gordon James and Adalbert Kerber, The representation theory of the symmetric group, CUP 1984
email: Jack Shotton