Hook removal operators on the odd Young graph

TL;DR

This paper investigates hook removal operators on odd partitions related to symmetric groups, completing previous work by analyzing their commutativity properties.

Contribution

It provides a complete characterization of the commutativity of hook removal operators on odd partitions, extending prior partial results.

Findings

Established conditions for commutativity of hook removal operators.

Completed the discussion initiated by previous researchers in 2016.

Contributed to the understanding of the structure of odd partitions in representation theory.

Abstract

In this article we consider hook removal operators on odd partitions, i.e., partitions labelling odd-degree irreducible characters of finite symmetric groups. In particular we complete the discussion, started by Isaacs, Navarro, Olsson and Tiep in 2016, concerning the commutativity of such operators.