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The Symmetric Group: Representation Theory and Combinatorics (LYLEU16SF)

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  • Full or part time
    Dr S Lyle
  • Application Deadline
    No more applications being accepted
  • Self-Funded PhD Students Only
    Self-Funded PhD Students Only

Project Description

The symmetric group S_n is one of the most universal and important objects in algebra. However, there are still many open questions surrounding it, in particular regarding its action on other objects. Over the complex numbers, we understand the irreducible S_n modules, but we still do not know what happens if we tensor a pair of them together, or the constituents of the Foulkes module. Over a field of prime characteristic, even less is known. Although it is possible to construct the irreducible modules, their dimension is not generally known.

This project looks to study the representation theory of the symmetric group algebra over fields of arbitrary characteristic, as well as looking at related problems in representation theory.

Funding Notes

This PhD project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources. Details of tuition fees can be found at

A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. The amount charged annually will vary considerably depending on the nature of the project and applicants should contact the primary supervisor for further information about the fee associated with the project.


i) G. D. James (1978). The Representation Theory of the Symmetric Groups, Lecture Notes in Mathematics 682, Springer.
ii) Bruce E. Sagan (2001). The symmetric group: Representations, Combinatorial Algorithms and Symmetric Functions, Springer graduate texts in mathematics.
iii) G. D. James and A. Kerber (1981). The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, vol. 16, Addison-Wesley, Reading, Mass.
iv) A. Mathas (1999). Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group, University Lecture Series 15, American Mathematical Society.

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