Generic Gelfand-Tsetlin representations of Uqtw(so3) and Uqtw(so4)

We construct generic Gelfand-Tsetlin representations of the iota quantum groups U-q(tw)(so(3)) and U-q(tw)(so(4)). These representations are infinite-dimensional analogs to the finite-dimensional irreducible representations provided by Gavrilik and Klimyk in [q-deformed orthogonal and pseudo-orthogonal algebras and their representations, Lett. Math. Phys. 21 (1991) 215-220]. They are quantum analogs of generic Gelfand-Tsetlin representations constructed by Mazorchuk in [On Gelfand-Zetlin modules over orthogonal Lie algebras, Algebra Colloq. 8 (2001) 345-360]. We give sufficient conditions for irreducibility and provide an upper bound for the length with the help of Casimir elements found by Molev, Ragoucy and Sorba.