On the Submodule Structure of Hook Specht Modules in Characteristic 2

2024/05/03 by Zain Ahmed Kapadia, Kapadia, Zain Ahmed
Mathematics · #05E10 #20C30 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2405.02039

openalex publication_date 2024/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The submodule structure of general Specht modules in prime characteristic is a difficult open problem. Kleshchev and Sheth [Journal of Algebra, 221(2), pp.705-722] gave a combinatorial description of the submodule structure of Specht modules labelled by 2-part partitions in prime characteristic. Using this result, as well as filtrations of Specht modules labelled by hook partitions via 2-part Specht modules in characteristic 2, one can study the submodule structure of hook Specht modules. In particular, we classify which of these are uniserial.

Related

• On the Submodule Structure of Hook Specht Modules in Characteristic 2 II
• On some trivial source Specht modules
• Homomorphisms from an arbitrary Specht module to one corresponding to a hook
• Specht modules labelled by hook bipartitions II
• On Integral Forms of Specht Modules Labelled by Hook Partitions