Tuesday, July 8, 14:00, 7.527
Eugenio Giannelli (London),
From Foulkes modules to the decomposition matrix of the symmetric group.
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