{"paper":{"title":"Symmetries of modules of differential operators","license":"","headline":"","cross_cats":["math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Hichem Gargoubi, Pierre Mathonet, Valentin Ovsienko (ICJ)","submitted_at":"2005-06-16T14:50:54Z","abstract_excerpt":"Let ${\\cal F}\\_\\lambda(S^1)$ be the space of tensor densities of degree (or weight) $\\lambda$ on the circle $S^1$. The space ${\\cal D}^k\\_{\\lambda,\\mu}(S^1)$ of $k$-th order linear differential operators from ${\\cal F}\\_\\lambda(S^1)$ to ${\\cal F}\\_\\mu(S^1)$ is a natural module over $\\mathrm{Diff}(S^1)$, the diffeomorphism group of $S^1$. We determine the algebra of symmetries of the modules ${\\cal D}^k\\_{\\lambda,\\mu}(S^1)$, i.e., the linear maps on ${\\cal D}^k\\_{\\lambda,\\mu}(S^1)$ commuting with the $\\mathrm{Diff}(S^1)$-action. We also solve the same problem in the case of straight line $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0506044","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"}