Modular representation theory of symmetric groups and their Hecke algebras

Summary

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

Supervisor(s)

Professor Andrew Mathas

Research Location

School of Mathematics and Statistics

Program Type

Masters/PHD

Synopsis

The reprsentation 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

The algebra group at University of Sydney is one of the most dynamic research groups in mathematics within Australia. The University of Sydney has one of the strongest concentrations of algebraists in the country and in representation theory the department ranks highly on the world stage.The algebra group at the University of Sydney hosts a very active weekly seminar series. Prominent international mathematicians regularly speak in our seminar. In addition, there is a constant stream of high powered international visitors who come to the department to collaborate and exchange ideas with the different members of the group. 

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Keywords

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

Opportunity ID

The opportunity ID for this research opportunity is: 593