Generic triangular solutions of the reflection equation: $U_{q}(\widehat{sl_2})$ case

TL;DR

This paper derives generic triangular boundary K-operators for the reflection equation using the triangular q-Onsager algebra and Borel subalgebras of U_q(sl_2), advancing understanding of integrable boundary conditions.

Contribution

It introduces a new method to construct triangular K-operators for the reflection equation based on the triangular q-Onsager algebra and Borel subalgebras of U_q(sl_2).

Findings

Derived explicit triangular K-operators solving the reflection equation.

Connected the solutions to the structure of the triangular q-Onsager algebra.

Provided a framework for analyzing boundary conditions in integrable models.

Abstract

We consider intertwining relations of the triangular $q$-Onsager algebra, and obtain generic triangular boundary $K$-operators in terms of the Borel subalgebras of $U_{q}(sl_2)$. These $K$-operators solve the reflection equation.