The multistep homology of the simplex and representations of symmetric groups

DOI10.1017/S0305004119000124zbMath1486.20015arXiv1803.00465OpenAlexW2964211715MaRDI QIDQ4958659

Mark Wildon

Publication date: 14 September 2021

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.00465

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Modular representations and characters (20C20) Homological methods in group theory (20J05) Simplicial sets and complexes in algebraic topology (55U10) Chain complexes (category-theoretic aspects), dg categories (18G35)

Uses Software

• Magma

Cites Work

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• Sylow subgroups of symmetric and alternating groups and the vertex of \(S^{(k p - p, 1^p)}\) in characteristic \(p\)
• On \(p\)-Kostka numbers and Young modules.
• Permutation resolutions for Specht modules.
• Characteristic-free resolutions of Weyl and Specht modules.
• Endomorphism rings of permutation modules over maximal Young subgroups.
• The vertices and sources of the basic spin module for the symmetric group in characteristic 2.
• On decomposability of some Specht modules for symmetric groups
• Representations of the symmetric groups over the field of order 2
• On the decomposition matrices of the symmetric groups. II
• The representation theory of the symmetric groups
• The Magma algebra system. I: The user language
• Two theorems of Gauss and allied identities proved arithmetically
• Green vertices and sources of simple modules of the symmetric group labelled by hook partitions.
• Spin Modules for Symmetric Groups
• Specht modules and the radical of the group ring over the symmetric group γ_p
• Hook representations of the symmetric groups

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