Algebraic study of quantum configuration spaces of decorated flags

Let $G$ be a connected, simply connected complex simple algebraic group and $\mathscr{A}_G=G/U^+$ its base affine space, whose elements are called decorated flags. We introduce the quantum configuration space of decorated flags $\mathcal{O}_q(\mathrm{Conf}_K \mathscr{A}_G)$ and initiate its algebrai