Simone Castellan: Towards K matrices for affine yangians

Tuesday Oct 6, 2026, 10:30 AM → 11:30 AM Europe/Paris

The Yang–Baxter equation (YBE) and the reflection equation (RE) are two fundamental symmetries in mathematics arising from particles moving along a line or a half-line. The quest for solutions of the YBE (called R-matrices) is at the very origin of the theories of quantum groups and Yangians. Similarly, solutions of the RE (called K-matrices) are closely related to quantum symmetric pairs and twisted Yangians. In this talk, I will give an overview of the YBE and RE and explain how quantum groups and their coideal subalgebras provide a framework for constructing solutions. I will then discuss the problem of constructing K-matrices for affine Yangians and outline an approach being investigated in an ongoing project with Andrea Appel.