学术报告（Bart Vlaar 2025.10.28）

摘要: We will survey recent developments and open problems in the algebraic theory of universal reflection equations and its application to quantum integrable systems with boundary conditions, which is one of its main motivations. The main class of examples is described by quantum symmetric pairs of affine type, a q-deformation of a pair (affine Lie algebra,fixedpoint subalgebra of a suitable involution). These were defined in general by Stefan Kolb but contain older examples as special cases, e.g. q-Onsager algebra and twisted q-Yangians. In finitedimensional representations, they provide trigonometric K-matrices in the same way as a quantum affine algebra provides trigonometric Rmatrices. Based on joint works with Andrea Appel and Robert Weston.