In this paper we study the modular structure of the Foulkes module H(2m) of the symmetric group S2m 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 H(2m). 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.
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Hall et al. (2024) studied this question.
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