The full set of $c_n$-invariant factorized $S$-matrices

TL;DR

This paper constructs the complete set of $c_n$-invariant factorized $S$-matrices using tensor product graphs, providing insights into their bootstrap structure and conserved charges.

Contribution

It introduces a method to explicitly construct all $c_n$-invariant factorized $S$-matrices via tensor product graphs, extending previous partial results.

Findings

Complete set of $c_n$-invariant $S$-matrices constructed

Analysis of bootstrap structure of these $S$-matrices

Discussion of Belavin's scalar Yangian conserved charges

Abstract

We use the method of the tensor product graph to construct rational (Yangian invariant) solutions of the Yang-Baxter equation in fundamental representations of $c_n$ and thence the full set of $c_n$-invariant factorized $S$-matrices. Brief comments are made on their bootstrap structure and on Belavin's scalar Yangian conserved charges.