Résumé

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.

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