Highest weight modules with respect to non-standard Gelfand-Tsetlin subalgebras

In this paper we study realizations of highest weight modules for the complex Lie algebra ${\mathfrak{g}\mathfrak{l}}_n$ with respect to non-standard Gelfand-Tsetlin subalgebras. We also provide sufficient conditions for such subalgebras to have a diagonalizable action on these realizations.