The Pelletier-Ressayre hidden symmetry for Littlewood-Richardson coefficients

TL;DR

This paper proves a conjectured identity for Littlewood-Richardson coefficients using a new birational involution applicable over any semifield, advancing understanding of algebraic symmetries.

Contribution

It introduces a novel birational involution and proves a conjectured symmetry for Littlewood-Richardson coefficients, expanding algebraic tools in representation theory.

Findings

Proved Pelletier-Ressayre conjecture on Littlewood-Richardson coefficients

Developed a new birational involution applicable over any semifield

Enhanced understanding of symmetries in algebraic combinatorics

Abstract

We prove an identity for Littlewood--Richardson coefficients conjectured by Pelletier and Ressayre (arXiv:2005.09877). The proof relies on a novel birational involution defined over any semifield.