4 problems

Bijection conjecture. The assignment $(X,\tau,\chi) \mapsto \theta(X,\tau,\chi)$ induces a bijection

Centre-generation conjecture. A single element of

Generalized Onsager presentation conjecture. The Lie algebra $\widetilde{\mathfrak k}$ is isomorphic to $\mathfrak k$.

Generalized Satake diagram classification conjecture. All such coideal subalgebras of $U_q(\mathfrak g)$ arise from generalized Satake diagrams.