The branching models of Kwon and Sundaram via flagged hives

TL;DR

This paper establishes a bijection between two branching models in algebraic combinatorics, introduces a new model using flagged hives, and leverages symmetry properties of Littlewood-Richardson coefficients.

Contribution

It proves a conjectured bijection between Kwon and Sundaram's models and introduces a novel branching model based on flagged hives.

Findings

Established a bijection between Kwon and Sundaram's branching models

Discovered a new branching model using flagged hives

Utilized symmetry of Littlewood-Richardson coefficients in hive model

Abstract

We prove a bijection between the branching models of Kwon and Sundaram, conjectured previously by Lenart-Lecouvey. To do so, we use a symmetry of Littlewood-Richardson coefficients in terms of the hive model. Along the way, we obtain a new branching model in terms of flagged hives.