Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators

TL;DR

This paper explores the augmented q-Onsager algebra, deriving boundary K-operators related to Baxter Q-operators, and analyzes their asymptotic representations and solutions to reflection equations.

Contribution

It introduces new boundary K-operators for the augmented q-Onsager algebra and connects them to Baxter Q-operators through asymptotic limits.

Findings

Derived generic boundary K-operators solving reflection equations.

Established limits of K-operators in Verma modules for Baxter Q-operators.

Connected algebraic structures to integrable models via reflection equations.

Abstract

We consider intertwining relations of the augmented $q$-Onsager algebra introduced by Ito and Terwilliger, and obtain generic (diagonal) boundary $K$-operators in terms of the Cartan element of $U_{q}(sl_2)$. These $K$-operators solve reflection equations. Taking appropriate limits of these $K$-operators in Verma modules, we derive $K$-operators for Baxter Q-operators and corresponding reflection equations.