Proof of the Newell-Littlewood saturation conjecture

TL;DR

This paper proves the saturation conjecture for Newell-Littlewood numbers by extending honeycomb combinatorics to a M"obius strip, generalizing prior work on Littlewood-Richardson coefficients.

Contribution

It introduces honeycombs on a M"obius strip to prove the saturation conjecture for Newell-Littlewood numbers, a significant generalization of previous combinatorial methods.

Findings

Proves the saturation conjecture for Newell-Littlewood numbers.

Extends honeycomb combinatorics to a M"obius strip setting.

Generalizes the saturation result from Littlewood-Richardson coefficients.

Abstract

By inventing the notion of honeycombs, A. Knutson and T. Tao proved the saturation conjecture for Littlewood-Richardson coefficients. The Newell-Littlewood numbers are a generalization of the Littlewood-Richardson coefficients. By introducing honeycombs on a M\"obius strip, we prove the saturation conjecture for Newell-Littlewood numbers posed by S. Gao, G. Orelowitz and A. Yong.