Abstract
Let \((R, \frak{m}, k_{R})\) be a regular local k-algebra satisfying the weak Jacobian criterion, and such that k R /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.
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Källström, R. \(\mathcal{D}\)-modules with finite support are semi-simple. Ark Mat 52, 291–299 (2014). https://doi.org/10.1007/s11512-013-0186-z
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DOI: https://doi.org/10.1007/s11512-013-0186-z