Abstract
Let $(R, \frak{m}, k_{R})$ be a regular local k-algebra satisfying the weak Jacobian criterion, and such that kR/k is an algebraic field extension. Let $\mathcal{D}_{R}$ be the ring of k-linear differential operators of R. We give an explicit decomposition of the $\mathcal{D}_{R}$-module $\mathcal{D}_{R}/\mathcal{D}_{R} \frak{m}_{R}^{n+1}$ as a direct sum of simple modules, all isomorphic to $\mathcal{D}_{R}/\mathcal{D}_{R} \frak{m}$, where certain “Pochhammer” differential operators are used to describe generators of the simple components.
Citation
Rolf Källström. "$\mathcal{D}$-modules with finite support are semi-simple." Ark. Mat. 52 (2) 291 - 299, October 2014. https://doi.org/10.1007/s11512-013-0186-z
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