6 problems

Let $V$ be the defining comodule, and let $V_4$ and $\overline{V}_{\!\!4}$ be the $U_q(\mathfrak{spo}(2\,|\,2))$-submodules of $V\otimes V$ considered in the paper. Let…

Inequivalence conjecture. The $R$-matrices for $Osp_q(N|2m)$ and $Osp'_q(2m|2n)$, together with the corresponding quantum groups, are inequivalent.

Let $U_q(osp(1|2))$ be the quantum supergroup, let $u,v\in\{0,1\}$, let $q=\exp[i\pi b^2]$, and let $\mathsf{x}$ and $\mathsf{p}$ be the position and momentum operators on…

Let ${\mathbf U}(\mathfrak{gl}_{m|1})$ be the quantum general linear supergroup, and consider its polynomial representations. In the nonsuper case, the canonical basis for the nega…

Affine PBW-basis conjecture. PBW-type bases can be constructed in affine type using methods similar to those in the cited work.

PBW-basis coincidence conjecture. These PBW bases should coincide.