A new way to evaluate MOY graphs

TL;DR

This paper introduces a novel method for evaluating MOY graphs, demonstrating its equivalence to classical methods and establishing a relationship between different Lie algebra evaluations.

Contribution

The paper presents a new evaluation technique for MOY graphs and proves its consistency with classical evaluations and a relation between $rak{sl}_N$ and $rak{sl}_{N-1}$ evaluations.

Findings

New evaluation method for MOY graphs

Proof of equivalence with classical evaluation

Relation between $rak{sl}_N$ and $rak{sl}_{N-1}$ evaluations

Abstract

We define a new way to evaluate MOY graphs. We prove that this new evaluation coincides with the classical evaluation by checking some skein relations. As a consequence, we prove a formula which relates the $\mathfrak{sl}_N$ and $\mathfrak{sl}_{N-1}$-evaluations of MOY graphs.