15 problems

Existence conjecture. There exists an element $K\in {\cal F}\otimes {\cal A}$ satisfying the relations specified subsequently in the source, namely the coaction/reflection relation…

Kirillov–Reshetikhin K-matrix conjecture. Symmetrizable invertible solutions of the generalized spectral reflection equation in tensor products of Kirillov–Reshetikhin modules, wit…

Meromorphicity conjecture. For all $V\in\mathcal{C}$, not necessarily irreducible, and for generic quantum symmetric pair parameters, $K_V(z)$ is the Laurent series expansion of a…

Generalized-parameter conjecture. For every $(\gamma,\sigma)\in\Gamma\Sigma_q$, the pair $(U_q(\mathfrak{g}),\mathcal{B}_{\gamma,\sigma})$ admits a cylindrical structure. Moreover,…

Spin-$j$ solution conjecture. Spin-$j$ fused K-operator solutions are unique up to an overall scalar factor, their matrix entries are linear combinations of monomials of the prescr…

Universal K-matrix evaluation conjecture. For every $j\in\frac{1}{2}\mathbb{N}$,

Arbitrary-spin uniqueness conjecture. The twisted intertwining relations determine uniquely the K-operators for any $j$, and these K-operators match the fused K-operators construct…

Universal K-matrix existence conjecture. A universal K-matrix $\mathfrak{K}$ for ${\cal A}_q$ satisfying the paper's axioms with the choice $\psi=\eta$ exists.

Parameter-inversion conjecture. There exists $g\in(U_q\mathfrak h)^{\mathcal W,\times}$ such that this relation is satisfied. Consequently, $k_{Y,\eta}$ specializes to a solution o…

Generalized Satake diagram classification conjecture. 1. If $K\in\operatorname{GL}(V)$ is a solution of the matrix reflection equation, then there exists a generalized Satake diagr…

Let $b,c,r,s,t,u$ be the indices occurring in the explicit formula for $Q_{b,c}(x,y,z,w)$, and let $C^{b,c}_{r,s,t,u}$ denote the coefficient defined there. From the preceding resu…

Type $B_3$ 3D reflection equation conjecture. The identity

Type B intertwiner transfer conjecture. The intertwiners $\mathscr{K}^B$ and $\mathscr{R}^B$ for $A_q(\mathrm{SO}_7)$ are obtained from the corresponding objects in…

Let $K$ denote a boundary matrix solving the reflection equation, and let $K(\lambda)$ be the particular $A_2^{(1)}$ SP matrix referred to as equation in the source. A limit proces…

The $A_2^{(1)}$ SP case concerns solutions $K$ of the reflection equation, where SP denotes the soliton-preserving boundary condition and a generic solution is non-degenerate, non-…