Complete branching rules for Specht modules

TL;DR

This paper provides a comprehensive combinatorial characterization of when Specht modules for arbitrary diagrams follow a complete branching rule, extending previous specific cases to all diagrams.

Contribution

It introduces a general combinatorial criterion based on maximal rectangles that determines the branching behavior of Specht modules for any diagram.

Findings

Provides a unified description for all diagrams' Specht module branching rules

Generalizes previous results for northwest and forest diagrams

Offers a practical combinatorial tool for analyzing Specht modules

Abstract

We give a combinatorial description for when the Specht module of an arbitrary diagram admits a (complete) branching rule. This description, given in terms of the maximal rectangles of the diagram, generalizes all previously known branching rules for Specht modules, such as those given by Reiner and Shimozono for northwest diagrams and by the present author for forest diagrams.