A hive model determination of multiplicity-free Schur function products and skew Schur functions

TL;DR

This paper uses the hive model, a combinatorial tool, to characterize all multiplicity-free products of Schur functions and skew Schur functions, providing a new perspective and confirming prior results.

Contribution

It applies the hive model to fully determine multiplicity-free Schur function products, offering a combinatorial understanding and confirming previous findings.

Findings

Confirmed all known multiplicity-free Schur products

Provided combinatorial conditions for multiplicity-freeness

Illustrated the hive model's effectiveness in representation theory

Abstract

The hive model is a combinatorial device that may be used to determine Littlewood-Richardson coefficients and study their properties. It represents an alternative to the use of the Littlewood-Richardson rule. Here properties of hives are used to determine all possible multiplicity-free Schur function products and skew Schur function expansions. This confirms the results of Stembridge, Gutschwager, and Thomas and Yong, and sheds light on the combinatorial origin of the conditions for being multiplicity-free, as well as illustrating some of the key features and power of the hive model.