On $A_{n-1}^{(1)},B_{n}^{(1)}, C_{n}^{(1)}, D_{n}^{(1)},A_{2n}^{(2)}, A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ Reflection $K$-Matrices

TL;DR

This paper classifies the most general regular solutions to boundary Yang-Baxter equations for vertex models linked to various affine Lie algebras, including reduced and diagonal solutions, with special cases analyzed separately.

Contribution

It provides a comprehensive classification of boundary K-matrices for affine Lie algebra-based vertex models, including reduced and diagonal solutions, expanding understanding of integrable boundary conditions.

Findings

Classified general regular solutions to boundary Yang-Baxter equations.

Presented reduced solutions via a limit procedure.

Listed diagonal K-matrices and analyzed special cases.

Abstract

We present the classification of the most general regular solutions to the boundary Yang-Baxter equations for vertex models associated with non-exceptional affine Lie algebras. Reduced solutions found by applying a limit procedure to the general solutions are discussed. We also present the list of diagonal $K$-matrices. Special cases are considered separately.