Regularization of Mickelsson generators for non-exceptional quantum groups

Let ${\mathfrak{g}}^{\mathrm{\prime }}\subset \mathfrak{g}$ be the pair of Lie algebras of either symplectic or orthogonal infinitesimal endomorphisms of the complex vector spaces ${\mathbb{C}}^{N-2}\subset {\mathbb{C}}^N$ and $U_q(\mathfrak{g}')\subset U_q(\mathfrak{g})$thepairofquantumgroupswithtriangulardecomposition$U_q(\mathfrak{g})=U_q(\mathfrak{g}-)U_q(\mathfrak{g}+)U_q(\mathfrak{h})$. Let $Z_q(\mathfrak{g},{\mathfrak{g}}^{\mathrm{\prime }})$ be the corresponding step algebra and regard its generators as rational trigonometric functions $\mathfrak{h}^*\to U_q(\mathfrak{g}_\pm)$. We describe their regularization such that the resulting generators do not vanish when specialized at any weight.