Specht Module
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High Quality Content by WIKIPEDIA articles! In mathematics, a Specht module is one of the representations of symmetric groups studied by Wilhelm Specht (1935). They are indexed by partitions, and in characteristic 0 the Specht modules of partitions of n form a complete set of irreducible representations of the symmetric group on n points. The elements ET can be considered as elements of the module V, by mapping each tableau to the tabloid it generates. The Specht module of the partition is the module generated by the elements ET as T runs through all tableaux of shape . The Specht module has a...
High Quality Content by WIKIPEDIA articles! In mathematics, a Specht module is one of the representations of symmetric groups studied by Wilhelm Specht (1935). They are indexed by partitions, and in characteristic 0 the Specht modules of partitions of n form a complete set of irreducible representations of the symmetric group on n points. The elements ET can be considered as elements of the module V, by mapping each tableau to the tabloid it generates. The Specht module of the partition is the module generated by the elements ET as T runs through all tableaux of shape . The Specht module has a basis of elements ET for T a standard Young tableau. Over fields of characteristic 0 the Specht modules are irreducible, and form a complete set of irreducible representations of the symmetric group. A partition is called p-regular if it does not have p parts of the same (positive) size. Over fields of characteristic p0 the Specht modules can be reducible. For p-regular partitions they havea unique irreducible quotient, and these irreducible quotients form a complete set of irreducible representations.
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