{"paper":{"title":"On bilinear invariant differential operators acting on tensor fields on the symplectic manifold","license":"","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Pavel Grozman","submitted_at":"2001-01-01T00:00:00Z","abstract_excerpt":"Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\\rho: GL(n)\\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\\subset M$, in other words, $T(V)$ is the space of tensor fields of type $V$ on $M$ on which the group $\\Diff (M)$ of diffeomorphisms of $M$ naturally acts. Elsewhere, the author classified the $\\Diff (M)$-invariant differential operators $D: T(V_{1})\\otimes T(V_{2})\\longrightarrow T(V_{3})$ for irreducible fibers with lowest weight. Here the result is generalized to bi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101266","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"}