Noncommutative LR coefficients and crystal reflection operators

TL;DR

This paper explores the relationship between noncommutative and classical Littlewood-Richardson coefficients using crystal reflection operators and combinatorics of frank words.

Contribution

It introduces a novel connection between noncommutative and classical LR coefficients through crystal reflection operators and frank words combinatorics.

Findings

Established a link between noncommutative and classical LR coefficients.

Utilized crystal reflection operators to relate these coefficients.

Highlighted the role of frank words in the combinatorial framework.

Abstract

We relate noncommutative Littlewood-Richardson coefficients of Bessenrodt-Luoto-van Willigenburg to classical Littlewood-Richardson coefficients via crystal reflection operators. A key role is played by the combinatorics of frank words.