A short geometric proof of a conjecture of Fulton

TL;DR

This paper presents a new geometric proof of Fulton's conjecture on Littlewood-Richardson coefficients, utilizing Horn's cones, offering an alternative to previous combinatorial and geometric proofs.

Contribution

It introduces a novel geometric proof of Fulton's conjecture based on Horn's cones, differing from prior combinatorial and geometric approaches.

Findings

Proof confirms Fulton's conjecture using Horn's cones

Provides an alternative geometric perspective to previous proofs

Enhances understanding of Littlewood-Richardson coefficients

Abstract

We give a new geometric proof of a conjecture of Fulton on the Littlewood-Richardson coefficients. This conjecture was firstly proved by Knutson, Tao and Woodward using the Honeycomb theory. A geometric proof was given by Belkale. Our proof is based on the geometry of Horn's cones.