Symmetric quasisymmetric Schur-like functions

TL;DR

This paper classifies the conditions under which certain quasisymmetric functions and their variants are symmetric, extending classical skew Schur functions.

Contribution

It provides a comprehensive classification of symmetry properties for dual immaculate, extended Schur, and advanced functions, including their skew versions.

Findings

Dual immaculate and extended Schur functions are symmetric under specific conditions.

Classical skew Schur functions are recovered as special cases.

The classification applies to both functions and their skew generalizations.

Abstract

In this paper we classify when (row-strict) dual immaculate functions and (row-strict) extended Schur functions, as well as their skew generalizations, are symmetric. We also classify when their natural variants, termed advanced functions, are symmetric. In every case our classification recovers classical skew Schur functions.