Generic Gelfand-Tsetlin modules of quantized and classical orthogonal algebras

We construct infinite-dimensional analogues of finite-dimensional simple modules the nonstandard q-deformed enveloping algebra Uq′(son) defined by Gavrilik and Klimyk, we do same for classical universal U(son). In this paper only consider case when q is not a root unity, q→1 case. Extending work Mazorchuk on son, provide rational matrix coefficients these both use with rationalized formulas to embed respective algebras into skew group shift operators. Casimir elements were given Iorgov, commutative subalgebra Γ⊂Uq′(son) generated corresponding Γ1⊂U(son). The images Γ Γ1 under their embeddings are equal invariant certain actions. facts show that Harish-Chandra