Gelfand-Tsetlin modules over gl(n) with arbitrary characters

A Gelfand-Tsetlin tableau T(v) induces a character χv of the Gelfand-Tsetlin subalgebra Γ of U=U(gl(n,C)). By a theorem due to Ovsienko, for each tableau T(v) there exists a finite number of nonisomorphic irreducible Gelfand-Tsetlin modules with χv in its support, though explicit examples of such modules are only known for special families of characters. In this article we build a family of Gelfand-Tsetlin modules parametrized by characters, such that each character appears in its corresponding module. We also find the support of these modules, with multiplicities.