On unitriangular basic sets for symmetric and alternating groups

DOI10.1016/J.JALGEBRA.2022.11.036OpenAlexW4313305608MaRDI QIDQ2685355

Olivier Brunat, Jean-Baptiste Gramain, Nicolas Jacon

Publication date: 21 February 2023

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.00815

zbMATH Keywords

basic setdecomposition matrix of the alternating groupsdecomposition matrix of the Hecke algebras

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Modular representations and characters (20C20)

Uses Software

• CHEVIE
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Cites Work

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• Representations of Hecke algebras at roots of unity.
• Graded decomposition numbers of Ariki-Koike algebras for blocks of small weight.
• A proof of the Mullineux conjecture
• CHEVIE -- A system for computing and processing generic character tables
• Derived equivalences for symmetric groups and \(\mathfrak{sl}_2\)-categorification.
• A basic set for the alternating group
• Bijections of p -Regular Partitions and p -Modular Irreducibles of the Symmetric Groups
• On properties of the Mullineux map with an application to Schur modules
• On mullineux' conjecture in the representation theory of symmetric groups
• Branching Rules for Modular Representations of Symmetric Groups III: Some Corollaries and a Problem of Mullineux

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