5 problems

Existence conjecture. There exists an action of the semi-direct product $B_n\ltimes\mathbb{Z}^n$ on ${\rm U}'_q(\mathfrak{sp}_{2n})$ analogous to the $B_N$-action on…

AII shifted twisted Yangian conjecture. A version of Theorems A and B should hold true for $beta=-1$ when $y_n^+(sigma)$ is replaced by the as-yet-undefined shifted twisted Yangian…

Let $D$ be a skew-affine generalized Weyl algebra of rank two, meaning that $D=T[t_1,t_2]$ for a finitely generated commutative $\mathbb{C}$-algebra $T$, with automorphisms…

The center conjecture. The center of $H_\zeta(\mathfrak{sp}_{2n})$ is

PBW basis parametrization conjecture. The lattice points in $\mathcal{C}(P,A)_{(\lambda,0)}$ parametrize a PBW basis of $V(\lambda)$ for the symplectic Lie algebras.