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In 2023, Petukhov and Sierra showed that Poisson primitive ideals of $\\mathrm{S}(W)$ and $\\mathrm{S}(V\\!ir)$ can be constructed from elements of $W^*$ and $V\\!ir^*$ of a particular form, called local functions. In this paper, we show how to use a local function on $W$ or $V\\!ir$ to construct a representation of the Lie algebra. 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