On the multiparametric {\cal U}_q[D_{n+1}^{(2)}] vertex model

TL;DR

This paper systematically studies multiparametric R-matrices and boundary Yang-Baxter equations for the {_{n+1}^{(2)}} vertex model, generalizing known K-matrix solutions with additional parameters and reflection types.

Contribution

It introduces a comprehensive analysis of multiparametric R- and K-matrices for the {
D_{n+1}^{(2)}} model, extending previous solutions with new free parameters and reflection configurations.

Findings

Derived new multiparametric K-matrix solutions

Generalized boundary Yang-Baxter equations

Expanded the class of admissible boundary conditions

Abstract

In this paper we consider families of multiparametric $R$-matrices to make a systematic study of the boundary Yang-Baxter equations in order to discuss the corresponding families of multiparametric $K$-matrices. Our results are indeed non-trivial generalization of the $K$-matrix solutions of the {\cal {U}}_{q}[D_{n+1}^{(2)}] vertex model when distinct reflections and extra free-parameters are admissible.