Description of coideal subalgebras for non-symmetrizable solutions

Determine the general structure and description of coideal subalgebras B ⊂ Uq(g) corresponding to non-symmetrizable invertible solutions of the generalized spectral reflection equation (6.6), including those not obtainable as limits of symmetrizable solutions.

Background

Beyond symmetrizable solutions, there exist non-symmetrizable invertible solutions to the spectral reflection equation that do not arise as limits of symmetrizable ones. While the triangular q-Onsager algebra (embedded into Uq(sl2)) has a known description, a general framework for the associated coideal subalgebras B in Uq(g) is lacking.

This open question seeks a unified structural description of the coideal subalgebras tied to such non-symmetrizable solutions, advancing both the theory of QSPs and boundary integrable systems.