Classification of $Q$-homogeneous skew Schur $Q$-functions

TL;DR

This paper classifies $Q$-homogeneous skew Schur $Q$-functions, establishing when they are scalar multiples of a single Schur $Q$-function, and introduces new tools applicable to broader classification problems.

Contribution

It provides a complete classification of $Q$-homogeneous skew Schur $Q$-functions and develops novel methods for analyzing skew Schur $Q$-functions.

Findings

Identifies all $Q$-homogeneous skew Schur $Q$-functions

Develops new tools for classifying skew Schur $Q$-functions

Facilitates further research in symmetric function classification

Abstract

We classify the $Q$-homogeneous skew Schur $Q$-functions, i.e., those of the form $Q_{\lambda/\mu} = k \cdot Q_{\nu}$. On the way we develop new tools that are useful also in the context of other classification problems for skew Schur $Q$-functions.