Abstract
Permutation modules play an important role in the representation theory of the symmetric group. Hartmann and Paget defined permutation modules for Brauer algebras. We generalise their construction to a wider class of algebras, namely cellularly stratified algebras, satisfying certain conditions. We give a decomposition into indecomposable summands, the Young modules, and show that permutation modules and Young modules admit cell filtrations (with well-defined filtration multiplicities). Partition algebras are shown to satisfy the given conditions, provided the characteristic of the underlying field is large enough. Thus we obtain a definition of permutation modules for partition algebras as an application.
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