On a conjecture of Khoroshkin and Tolstoy

TL;DR

This paper proves a no-go theorem that disproves a conjecture by Khoroshkin and Tolstoy regarding the factorization of the lower triangular part in the Gaussian decomposition of the Yangian's universal R-matrix, advancing understanding in quantum algebra.

Contribution

It provides a negative result that clarifies the limitations of factorization in the Yangian's R-matrix decomposition, addressing a longstanding conjecture.

Findings

Disproves the conjecture of Khoroshkin and Tolstoy

Establishes a no-go theorem for factorization

Clarifies the structure of the Yangian's R-matrix

Abstract

We prove a no-go theorem on the factorization of the lower triangular part in the Gaussian decomposition of the Yangian's universal $R$-matrix, yielding a negative answer to a conjecture of Khoroshkin and Tolstoy from [Lett. Math. Phys. vol. 36 1996].