Abstract
In this paper we study the modular structure of the permutation module H(2n) of the symmetric group S2n 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 characterise 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 S2n and that this summand exhibits many of the extensions between simple modules in its block.
Original language | English |
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Pages (from-to) | 2969–2984 |
Number of pages | 16 |
Journal | Journal of Pure and Applied Algebra |
Volume | 220 |
Issue number | 8 |
Early online date | 15 Feb 2016 |
DOIs | |
Publication status | Published - Aug 2016 |