{"paper":{"title":"D-modules on G-representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Philibert Nang","submitted_at":"2014-04-16T11:34:57Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4212","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}