  For any positive integer $n$, let
$W_n=\text{Der}(\mathbb{C}[t_1,\dots,t_n])$. The subspaces
$\mathfrak{h}_n=\text{Span}\{t_1\frac{\partial}{\partial{t_1}},\dots,t_n\frac{\partial}{\partial{t_n}}\}$
and
$\Delta_n=\text{Span}\{\frac{\partial}{\partial{t_1}},\dots,\frac{\partial}{\partial{t_n}}\}$
are two abelian subalgebras of $W_n$. We show that a full subcategory
$\Omega_{\mathbf{1}}$ of the category of $W_n$-modules $M$ which are locally
finite over $\Delta_n$ is equivalent to some full subcategory of weight
$W_n$-modules $M$ which are cuspidal modules when restricted to the subalgebra
$\mathfrak{sl}_{n+1}$ of $W_n$.
