From Foulkes modules to the decomposition matrix of the symmetric groups

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• Eugenio Giannelli
• Friday 14 February 2014, 15:00-16:00
• CMS, MR5.

If you have a question about this talk, please contact Julian Brough.

The determination of the decomposition numbers of symmetric groups is a famous long-standing open problem. In this talk I will firstly introduce my recent joint work with Dr. Wildon on the topic. We have been studying some structural properties of the family of p-permutation modules known as Foulkes modules; I will show how we used this information to completely determine a number of columns of the decomposition matrix of the symmetric group. In the second part of the talk I will present a new, more general result on the modular structure of the Foulkes modules. In particular I will give a classication of the vertices of all their indecomposable summands.

This talk is part of the Junior Algebra and Number Theory seminar series.

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