Boundary transfer matrices arising from quantum symmetric pairs

2024/10/29 by Appel, Andrea, Vlaar, Bart · 1 citation
#16T25 #17B37 #81R12 #81R50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2410.21654

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.

Cited by

• Universal TT- and TQ-relations via centrally extended q-Onsager algebra

Related

• Infinite dimensional symmetry of corner transfer matrices
• Boundary K-matrix for the quantum Mikhailov-Shabat model
• Vertex operators for boundary algebras
• On integrability of a q-oscillator lattice with a B-boundary
• Boundary conditions for integrable quantum systems