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This paper is devoted to an elementary new construction of $1$-singularGelfand-Tsetlin modules using complex geometry. We introduce a universal ring$\mathcal D_o$ together with the vector space $\mathcal S=\mathcal S(\mathcalD_o)$ with basis $\mathcal B_o = \mathcal B(\mathcal D_o)$ formed from somelocal distributions such that $\mathcal S$ is a natural $\mathcal D_o$-module.For any homomorphism of rings $\mathcal U(\mathfrak{h}) \to \mathcal D_o$,where $\mathfrak{h}$ is a Lie algebra, it follows that $\mathcal S$ is also an$\mathfrak{h}$-module. We observe that the homomorphism of rings constructed in[FO] is a homomorphism of type $\mathcal U(\mathfrak{gl}_n(\mathbb C)) \to\mathcal D_o$. Using this observation we obtain a construction of the universal$1$-singular Gelfand-Tsetlin $\mathfrak{gl}_n(\mathbb C)$-module from [FRG].

A geometric approach to $1$-singular Gelfand-Tsetlin $\mathfrak {gl}_n$-modules