The restriction of a Specht module to a smaller symmetric group has afiltration by Specht modules of this smaller group. In the cellular structureof the group algebra of the symmetric group, the cell modules are exactly theSpecht modules. The partition algebra is a cellular algebra containing thegroup algebra of the symmetric group. In this article, we study the structureof the restriction of a cell module to the group algebra of a symmetric group(with smaller index) and show that it has Specht filtration if thecharacteristic of the field is large enough.
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