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Does the normal ordered product on differential operators lift to $U\left(\mathfrak{gl}_n\right)$?
Let $n\in\mathbb N$. Let $k$ be a commutative ring in which $1,2,3,\ldots$ are invertible. Let $\Omega$ denote the $k$-algebra of polynomial differential operators on $n$ variables $x_1$, $x_2$, ..., $...
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