Boundary transfer matrices arising from quantum symmetric pairs

TL;DR

This paper develops a universal framework for boundary transfer matrices in quantum integrable systems, connecting quantum symmetric pairs and reflection equations, and recovers known constructions in finite type.

Contribution

It introduces a new universal approach to boundary transfer matrices using quantum symmetric pairs, unifying and extending previous methods.

Findings

Framework applicable to finite and affine types

Recovers Kolb's construction in finite type

Highlights open problems in reflection equation solutions

Abstract

We introduce a universal framework for boundary transfer matrices, inspired by Sklyanin's two-row transfer matrix approach for quantum integrable systems with boundary conditions. The main examples arise from quantum symmetric pairs of finite and affine type. As a special case we recover a construction by Kolb in finite type. We review recent work on universal solutions to the reflection equation and highlight several open problems in this field.