Tuesday, July 8, 14:00, 7.527

Eugenio Giannelli (London),
From Foulkes modules to the decomposition matrix of the symmetric group.

Abstract:
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 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 Green vertices of all their indecomposable summands.