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Combinatorial Representation Theory: Partitions and Basic Sets


Project Description

The representation theory of many families of finite groups can be presented in terms of combinatorial objects. The most famous example is the symmetric groups, where the irreducible complex representations are parametrized by partitions. Other groups, such as the double covers of symmetric and alternating groups, or the infinite family of complex reflection groups, require the use of bar-partitions, or of tuples of partitions with certain properties.

The aim of this project is to develop a fuller understanding of these combinatorial objects, and to use it to better describe the representation theory of groups such as complex reflection groups, or the general linear group.

Of particular interest is the concept of basic set, which can provide some insight in the modular representation theory of finite groups (i.e. over fields of prime characteristic), while in fact working solely over fields of characteristic zero. One major component of this project will be the description of basic sets for various infinite families of finite groups, and their use for producing new information about the decomposition matrices and Brauer characters of these groups.

Candidates should have (or expect to achieve) a UK honours degree at 2.1 or above (or equivalent) in (Pure) Mathematics.

It is essential that the successful applicant has a background in algebra and knowledge of group theory and representation theory of groups.

APPLICATION PROCEDURE:

• Apply for Degree of Doctor of Philosophy in Mathematics
• State name of the lead supervisor as the Name of Proposed Supervisor
• State ‘Self-funded’ as Intended Source of Funding
• State the exact project title on the application form

When applying please ensure all required documents are attached:

• All degree certificates and transcripts (Undergraduate AND Postgraduate MSc-officially translated into English where necessary)
• Detailed CV
• Details of 2 academic referees

Informal inquiries can be made to Dr J-B Gramain ( ) with a copy of your curriculum vitae and cover letter. All general enquiries should be directed to the Postgraduate Research School ()

Funding Notes

This project is advertised in relation to the research areas of the discipline of Mathematics. The successful applicant will be expected to provide the funding for Tuition fees, living expenses and maintenance. Details of the cost of study can be found by visiting View Website. THERE IS NO FUNDING ATTACHED TO THESE PROJECTS.

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