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On the Submodule Structure of Hook Specht Modules in Characteristic 2 II

Zain Ahmed Kapadia

Abstract

We classify which 2-part Young modules in characteristic 2 are uniserial, and which hook Specht modules in characteristic 2 are direct sums of uniserial summands. This is a continuation of the author's previous work [arxiv:2405.02039].

On the Submodule Structure of Hook Specht Modules in Characteristic 2 II

Abstract

We classify which 2-part Young modules in characteristic 2 are uniserial, and which hook Specht modules in characteristic 2 are direct sums of uniserial summands. This is a continuation of the author's previous work [arxiv:2405.02039].

Paper Structure

This paper contains 4 sections, 13 theorems, 6 equations.

Table of Contents

  1. Introduction
  2. Background
  3. Uniserial $2$-part Young modules
  4. Hook Specht modules which are direct sums of uniserial summands

Key Result

Theorem 3.3

kapadia2024submodule Let $\lambda = (\lambda_1, \lambda_2) \vdash n.$ If $\alpha := \lambda_1 - \lambda_2 + 1$ has at least two non-zero digits in its binary expansion, define $a := \nu_2(\alpha), b := \nu_2(\alpha + 2^{\nu_2(\alpha)}),$ and $c := \nu_2(\alpha - 2^{\nu_2(\alpha)}).$ That is, $a$ is

Theorems & Definitions (30)

  • Definition 3.1
  • Definition 3.2
  • Theorem 3.3
  • Corollary 3.4
  • proof
  • Definition 3.5
  • Theorem 3.6
  • Theorem 3.7
  • Corollary 3.8
  • proof
  • ...and 20 more