Bart Vlaar

collaborators

4 papers

math.RT2025

Tensor K-matrices for quantum symmetric pairs

Andrea Appel, Bart Vlaar

Let $g$ be a symmetrizable Kac-Moody algebra, $U_{q} (g)$ its quantum group, and $U_{q} (k) \subset U_{q} (g)$ a quantum symmetric pair subalgebr…

math.RT2025

Trigonometric K-matrices for finite-dimensional representations of quantum affine algebras

Andrea Appel, Bart Vlaar

Let $g$ be a complex simple Lie algebra and $U_{q} (g^)$ the corresponding quantum affine algebra. We prove that every irreducible finite-dimensional $U_q(\…

math.RT2025

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.…

math.RT2025

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 $H$ endowed with a universal K-matrix, i.e., a universal solution of a generalized reflecti…