Regularization of Mickelsson generators for nonexceptional quantum groups

Abstract

Let g′ ⊂ g be a pair of Lie algebras of either symplectic or orthogonal infinitesimal endomorphisms of the complex vector spaces C^N−2 ⊂ C^Nand U_q(g′) ⊂ U_q(g) be a pair of quantum groups with a triangular decompositionU_q(g) = U_q(g_-)U_q(g₊)U_q(h). LetZ_q(g, g′) be the corresponding step algebra. We assume that its generators are rational trigonometric functions h ∗ → U_q(g_±). We describe their regularization such that the resulting generators do not vanish for any choice of the weight.