  We give an answer to the abstract Capelli problem: Let $(G, V)$ be a
multiplicity-free finite-dimensional representation of a connected reductive
complex Lie group $G$ and $G'$ be its derived subgroup. Assume that the
categorical quotient $V//G$ is one dimensional, i.e., there exists a polynomial
$f$ generating the algebra of $G'$-invariant polynomials on $V$
($\mathbb{C}[V]^{G'} = \mathbb{C}[f]$) and that $f \not\in \mathbb{C}[V]^{G}$.
We prove that the category of regular holonomic $\mathcal{D}_{V}$-modules
invariant under the action of $G$ is equivalent to the category of graded
modules of finite type over a suitable algebra $\mathcal{A}$.
