Set families and Foulkes modules

DOI10.1007/s10801-011-0282-8zbMath1229.05281arXiv1007.2946OpenAlexW2158902365MaRDI QIDQ644687

Mark Wildon, Rowena Paget

Publication date: 7 November 2011

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.2946

zbMATH Keywords

Specht moduleclosed set familyFoulkes moduleFoulkes' conjecturemodule homomorphism

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

Related Items (7)

Foulkes modules and decomposition numbers of the symmetric group. ⋮ Projective indecomposable permutation modules ⋮ On the decomposition of the Foulkes module. ⋮ On permutation modules and decomposition numbers of the symmetric group. ⋮ A \(q\)-analog of Foulkes' conjecture ⋮ Strong forms of self-duality for Hopf monoids in species ⋮ Minimal and maximal constituents of twisted Foulkes characters

Cites Work

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• \((\mathrm{GL}_n,\mathrm{GL}_m)\)-duality and symmetric plethysm
• The representation theory of the symmetric groups
• Stable properties of plethysm: On two conjectures of Foulkes
• On a conjecture of Foulkes
• On plethysm conjectures of Stanley and Foulkes
• Some Computations Regarding Foulkes' Conjecture
• Concomitants of the Quintic and Sextic Up To Degree Four in the Coefficients of the Ground Form
• On Symmetrized Kronecker Powers and the Structure of the Free Lie Ring

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