29 citations · 132 across the 18 of their papers we have counts for
18 papers
Boundary transfer matrices arising from quantum symmetric pairs
Andrea Appel, Bart Vlaar
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.…
Tensor K-matrices for quantum symmetric pairs
Andrea Appel, Bart Vlaar
Let be a symmetrizable Kac-Moody algebra, its quantum group, and a quantum symmetric pair subalgebr…
A Q-operator for open spin chains II: boundary factorization
Alec Cooper, Bart Vlaar, Robert Weston
One of the features of Baxter's Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral paramet…
Trigonometric K-matrices for finite-dimensional representations of quantum affine algebras
Andrea Appel, Bart Vlaar
Let be a complex simple Lie algebra and the corresponding quantum affine algebra. We prove that every irreducible finite-dimensional $U_q(\…
Quasi-bialgebras from set-theoretic type solutions of the Yang-Baxter equation
Anastasia Doikou, Alexandros Ghionis, Bart Vlaar
We examine classes of quantum algebras emerging from involutive, non-degenerate set-theoretic solutions of the Yang-Baxter equation and their q-analogues. After providing some univ…
Pseudo-symmetric pairs for Kac-Moody algebras
Vidas Regelskis, Bart Vlaar
Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces and real forms of complex Lie algebras, and are well-studied in the context of symmetrizable…
Universal K-matrices for quantum Kac-Moody algebras
Andrea Appel, Bart Vlaar
We introduce the notion of a cylindrical bialgebra, which is a quasitriangular bialgebra endowed with a universal K-matrix, i.e., a universal solution of a generalized reflecti…
A Q-operator for open spin chains I: Baxter's TQ relation
Bart Vlaar, Robert Weston
We construct a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter's TQ relation. Key roles in the…
Quasitriangular coideal subalgebras of in terms of generalized Satake diagrams
Vidas Regelskis, Bart Vlaar
Let be a finite-dimensional semisimple complex Lie algebra and an involutive automorphism of . According to G. Letzter, S. Kolb and M. Balagović th…
Solutions of the reflection equations
Vidas Regelskis, Bart Vlaar
We find the complete set of invertible solutions of the untwisted and twisted reflection equations for the Bazhanov-Jimbo R-matrix of type . We also show t…
Integral solutions to boundary quantum Knizhnik-Zamolodchikov equations
Nicolai Reshetikhin, Jasper Stokman, Bart Vlaar
We construct integral representations of solutions to the boundary quantum Knizhnik-Zamolodchikov equations. These are difference equations taking values in tensor products of Verm…
Reflection matrices, coideal subalgebras and generalized Satake diagrams of affine type
Vidas Regelskis, Bart Vlaar
We present a generalization of the theory of quantum symmetric pairs as developed by Kolb and Letzter. We introduce a class of generalized Satake diagrams that give rise to (not ne…
Boundary transfer matrices and boundary quantum KZ equations
Bart Vlaar
A simple relation between inhomogeneous transfer matrices and boundary quantum KZ equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogo…
Boundary quantum Knizhnik-Zamolodchikov equations and fusion
Nicolai Reshetikhin, Jasper Stokman, Bart Vlaar
In this paper we extend our previous results concerning Jackson integral solutions of the boundary quantum Knizhnik-Zamolodchikov equations with diagonal K-operators to higher-spin…
Koornwinder polynomials and the XXZ spin chain
Jasper Stokman, Bart Vlaar
Nonsymmetric Koornwinder polynomials are multivariable extensions of nonsymmetric Askey-Wilson polynomials. They naturally arise in the representation theory of (double) affine Hec…
Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors
Nicolai Reshetikhin, Jasper Stokman, Bart Vlaar
Solutions to boundary quantum Knizhnik-Zamolodchikov equations are constructed as bilateral sums involving "off-shell" Bethe vectors in case the reflection matrix is diagonal and o…
A non-symmetric Yang-Baxter algebra for the quantum nonlinear Schrödinger model (PhD Thesis)
Bart Vlaar
We study certain non-symmetric wavefunctions associated to the quantum nonlinear Schrödinger (QNLS) model, introduced by Komori and Hikami using representations of the degenerate a…
A non-symmetric Yang-Baxter Algebra for the Quantum Nonlinear Schrödinger Model
Bart Vlaar
We study certain non-symmetric wavefunctions associated to the quantum nonlinear Schrödinger model, introduced by Komori and Hikami using Gutkin's propagation operator, which invol…