Canonical bases arising from $\imath$quantum covering groups

Abstract

For $\imath$quantum covering groups $(\mathbf{U}, \mathbf{U}^\imath)$ of super Kac-Moody type, we construct $\imath$-canonical bases for the highest weight integrable $\mathbf{U}$-modules and their tensor products regarded as $\mathbf{U}^\imath$-modules, as well as a canonical basis for the modified form of the $\imath$quantum group $\mathbf{U}^\imath$, using the $\imath^\pi$-divided powers, rank one canonical basis for $\mathbf{U}^\imath$.