Modular representation theory of symmetric groups and their Hecke algebras


The representation theory of the symmetric groups is a very dynamic and active field with many challenging open problems.


Professor Andrew Mathas

Research Location

School of Mathematics and Statistics

Program Type



The representation theory of the symmetric group over fields of characteristic zero is very well understood. The irreducible modules and their characters have been completely determined for a long time and few problems remain in this area. On contrast, relatively little is known about the representations of the symmetric groups over fields of positive characteristic. for example, even though we know how to construct all of the irreducible representations over these fields the dimensions of these representations are unknown except in some very special cases. One of the central problems in this area is computing the decomposition matrices which, roughly speaking, describe how the ordinary irreducble representations decompose in positive characteristic.

Additional Information

HDR Inherent Requirements

In addition to the academic requirements set out in the Science Postgraduate Handbook, you may be required to satisfy a number of inherent requirements to complete this degree. Example of inherent requirement may include:

- Confidential disclosure and registration of a disability that may hinder your performance in your degree;
- Confidential disclosure of a pre-existing or current medical condition that may hinder your performance in your degree (e.g. heart disease, pace-maker, significant immune suppression, diabetes, vertigo, etc.);
- Ability to perform independently and/or with minimal supervision;
- Ability to undertake certain physical tasks (e.g. heavy lifting);
- Ability to undertake observatory, sensory and communication tasks;
- Ability to spend time at remote sites (e.g. One Tree Island, Narrabri and Camden);
- Ability to work in confined spaces or at heights;
- Ability to operate heavy machinery (e.g. farming equipment);
- Hold or acquire an Australian driver’s licence;
- Hold a current scuba diving license;
- Hold a current Working with Children Check;
- Meet initial and ongoing immunisation requirements (e.g. Q-Fever, Vaccinia virus, Hepatitis, etc.)

You must consult with your nominated supervisor regarding any identified inherent requirements before completing your application.

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Algebra, combinatorics, Hecke algebras, Schur algebras, symmetric groups., representation theory

Opportunity ID

The opportunity ID for this research opportunity is: 593