Boundary transfer matrices arising from quantum symmetric pairs
arXiv:2410.21654 · doi:10.1016/j.indag.2025.05.008
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.
Minor edits. Final version. 32 p
References in corpus (22)
- Quantum symmetric Kac-Moody pairs
- Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras
- Algebraic Structures Related to Reflection Equations
- The half-infinite XXZ chain in Onsager's approach
- Baxter's Relations and Spectra of Quantum Integrable Models
- Canonical bases for tensor products and super Kazhdan-Lusztig theory
- q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations
- Asymptotic representations and Drinfeld rational fractions
- Coideal subalgebras in quantum affine algebras
- Convex Bases of PBW type for Quantum Affine Algebras
- The bar involution for quantum symmetric pairs
- Constant Solutions of Reflection Equations and Quantum Groups
- Universal K-matrices for quantum Kac-Moody algebras
- Cyclotomic associators and finite type invariants for tangles in the solid torus
- Braided module categories via quantum symmetric pairs
- Boundary transfer matrices and boundary quantum KZ equations
- Quasitriangular coideal subalgebras of in terms of generalized Satake diagrams
- A Drinfeld type presentation of affine quantum groups II: split BCFG type
- Coxeter categories and quantum groups
- Ribbon braided module categories, quantum symmetric pairs and Knizhnik-Zamolodchikov equations
- Braid group action and quasi-split affine quantum groups I
- Tensor K-matrices for quantum symmetric pairs