This paper constructs a Specht filtration of permutation modules indexed by partitions, suggesting significant connections in affine type A and quiver theory.
In type A, Kleshchev-Ram-Mathas realize Specht modules as quotient of Permutation modules, in this paper, we construct a Specht filtration of Permutation modules indexed by hook partition in affine type A; and construct a generalized Specht filtration of Permutation modules indexed by any partition in linear quiver case.
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Tao Qin (2025) studied this question.
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