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 <a href="http://Appel.

https://indico.math.cnrs.fr/event/16484/ » target= »_blank » title= »Appel.

https://indico.math.cnrs.fr/event/16484/ »>Appel.

https://indico.math.cnrs.fr/event/16484/