Andrea Appel (Università di Parma)

In the last ten years, there has been a renewed interest in the theory of quantum symmetric pairs (QSPs). As the name suggests, a QSP is an algebraic datum which quantizes the notion of symmetric space. It consists of a Drinfeld-Jimbo quantum group of a simple Lie algebra and a distinguished coideal subalgebra quantizing the fixed point subalgebra of an involution. Although their representation theory remains quite mysterious, it is becoming more and more evident that QSPs possess an incredibly rich structure with their own theory of canonical basis and braid group actions yet adapted to a particular “boundary behavior”. In the first part of the talk, I will give an overview of this emerging theory, while in the second part I will report on ongoing joint work with B. Vlaar and T. Przezdziecki devoted to the construction of a meromorphic boundary Yang-Baxter operator for quantum affine symmetric pairs and a quantum Schur-Weyl duality which arises from the study of its poles.