Kauffman polynomial from a generalized Yang-Yang function

TL;DR

This paper derives braiding and fusion matrices from a generalized Yang-Yang function for certain Lie algebras and proves that the resulting knot invariants are equivalent to the Kauffman polynomial.

Contribution

It introduces a novel method to obtain Kauffman polynomial knot invariants using generalized Yang-Yang functions for specific Lie algebra representations.

Findings

Derived braiding and fusion matrices for type B, C, D Lie algebras

Proved the knot invariants correspond to Kauffman polynomial

Established a new link between Yang-Yang functions and knot invariants

Abstract

For the fundamental representations of the simple Lie algebras of type $B_{n}$, $C_{n}$ and $D_{n}$, we derive the braiding and fusion matrices from the generalized Yang-Yang function and prove that the corresponding knot invariants are Kauffman polynomial.