Let g be a complex simple finite-dimensional Lie algebra and Uₐ (g) the corresponding quantum affine algebra. We prove that every irreducible finite-dimensional Uₐ (g) -module gives rise to a family of trigonometric solutions of Cherednik’s generalized reflection equation. These depend on the choice of a quantum affine symmetric pair Uₐ (k) Uₐ (g). Our result relies on the construction of universal K-matrices for arbitrary quantum symmetric pairs we obtained in Represent. Theory 26, 764–824 (2022) and the fact that every irreducible Uₐ (g) -module is generically irreducible under restriction to Uₐ (k). In the case of small modules and Kirillov–Reshetikhin modules, we obtain new solutions of the standard and the transposed reflection equations.
Appel et al. (Mon,) studied this question.