Project: In the past decade, the foundational contributions of Letzter and Kolb have sparked a renewed interest within the mathematical community in the theory of quantum symmetric pairs (QSP). Roughly, a QSP algebra is to a symmetric space what a quantum group is to a Poisson-Lie group. More precisely, a QSP is the datum of a quantum group and a coideal subalgebra which quantizes the Lie subalgebra of fixed points corresponding to an involutive Lie algebra automorphism.

Despite the impetus of recent advancements, the overall understanding of the representation theory of quantum affine symmetric pairs is still partial and unsatisfactory. During the stay at ESI, we will try to develop a boundary analogue of the theory of q-characters as a tool to study the finite-dimensional representation theory of quantum affine algebras.

Research Team: Andrea Appel (U of Parma), Jianrong Li (U of Vienna), Tomasz Przezdziecki (U of Edinburgh), Bart Vlaar (BIMSA, Beijing)

Dates of Stay: June 8 - June 21, 2025 and January 11 - 24, 2026