Abstract
In this paper we study the modular structure of the Foulkes module of the symmetric group
acting on set partitions of a set of size 2m into m sets each of size 2, defined over a field of positive characteristic p. We aim to understand the decomposition of the tensor powers of
. In particular, we study the asymptotics of the non-projective part of tensor powers of these modules by computing the gamma invariant as defined by Dave Benson and Peter Symonds.
2020 Mathematics Subject Classification: