{"paper":{"title":"On the asymptotic S_n-structure of invariant differential operators on symplectic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.SG","authors_text":"Qingchun Ren, Travis Schedler","submitted_at":"2010-06-01T23:55:18Z","abstract_excerpt":"We consider the space of polydifferential operators on n functions on symplectic manifolds invariant under symplectic automorphisms, whose study was initiated by Mathieu in 1995. Permutations of inputs yield an action of S_n, which extends to an action of S_{n+1}. We study this structure viewing n as a parameter, in the sense of Deligne's category. For manifolds of dimension 2d, we show that the isotypic part of this space of <= 2d+1-th tensor powers of the reflection representation h=C^n of S_{n+1} is spanned by Poisson polynomials. We also prove a partial converse, and compute explicitly the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0268","kind":"arxiv","version":3},"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"}