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Greene's Theorem and ideals of the group algebra of a symmetric group

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arxiv 2412.01627 v1 pith:SYFHU6AH submitted 2024-12-02 math.RT

Stephen Donkin This is my paper · ORCID
classification math.RT
keywords groupsymmetricalgebracertainannihilatorbaseselementsfactor
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We show that certain factor rings of the group algebra of a symmetric group have natural bases of group elements. We also give generators for the annihilator of certain permutation modules for symmetric groups.

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  1. Rook sums in the symmetric group algebra

    math.CO 2025-07 conditional novelty 6.0 of 10

    Rook sums in the symmetric group algebra satisfy an explicit product rule, have linearly factorable minimal polynomials, and generate ideals whose sizes count pattern-avoiding permutations.

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