Classification of symmetrizable solutions of the spectral reflection equation in KR modules

Characterize symmetrizable invertible solutions of the generalized spectral reflection equation (6.6) in tensor products of Kirillov–Reshetikhin modules, with twist equal to a diagram automorphism, as rescaled actions of the grading-shifted universal K-matrix associated to quantum symmetric pairs with generalized parameter constraints as in Section 5.4.

Background

Kirillov–Reshetikhin (KR) modules form a fundamental class of finite-dimensional representations of quantum affine algebras. Spectral reflection equations govern boundary scattering in integrable models, and many known solutions arise from universal K-matrices linked to QSPs.

This conjecture posits a classification of symmetrizable invertible solutions in KR tensor products in terms of universal K-matrix actions with generalized parameter constraints (TEq), thereby connecting explicit solutions in integrable models to the universal QSP framework.