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Some Properties of Generalized Foulkes Module

Pál Hegedüs, Sai Praveen Madireddi

Abstract

Describing the decomposition of Foulkes module $F_b^a$ into irreducible Specht modules is an open problem for $a,b > 3$. In this article we provide a new approach for the Generalized Foulkes module $F_ν^a$ (with arbitrary partition $ν$ of $b$) through its restriction to a maximal Young subgroup ${S_b \times S_{ab -b}}$.

Some Properties of Generalized Foulkes Module

Abstract

Describing the decomposition of Foulkes module into irreducible Specht modules is an open problem for . In this article we provide a new approach for the Generalized Foulkes module (with arbitrary partition of ) through its restriction to a maximal Young subgroup .

Paper Structure

This paper contains 6 sections, 10 theorems, 36 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Properties of $U_{\nu, a}$
  4. Consequences for the Generalized Foulkes Module
  5. Concluding remarks and questions
  6. Acknowledgement

Key Result

Theorem 1

Let $k=b$ and as above, $U_{\nu,a}=V_{\nu,a}^{(1^b)}$. Then In particular, for $a=2$

Theorems & Definitions (21)

  • Theorem 1
  • Corollary 2
  • Corollary 3
  • Definition 4
  • Lemma 5
  • proof
  • Lemma 6
  • proof
  • Definition 7
  • Definition 8
  • ...and 11 more