Indecomposable summands of Foulkes modules

2015/08/22 by Giannelli, Eugenio, Wildon, Mark
#20C20 #20C30 #FOS: Mathematics #Representation Theory (math.RT) #Secondary: 05A17

paper · doi:10.48550/arxiv.1508.05498

Abstract

In this paper we study the modular structure of the permutation module H⁽²ⁿ⁾ of the symmetric group S_2n acting on set partitions of a set of size 2n into n sets each of size 2, defined over a field of odd characteristic p. In particular we characterize the vertices of the indecomposable summands of H⁽²ⁿ⁾ and fully describe all of its indecomposable summands that lie in blocks of p-weight at most two. When 2n < 3p we show that there is a unique summand of H⁽²ⁿ⁾ in the principal block of S_2n and that this summand exhibits many of the extensions between simple modules in its block.

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