{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:E5ZPUY7T2ZBGEYZETFAAJ6ATVE","short_pith_number":"pith:E5ZPUY7T","schema_version":"1.0","canonical_sha256":"2772fa63f3d642626324994004f813a92730f6b48871f6666b57cf2f5122259e","source":{"kind":"arxiv","id":"1006.0268","version":3},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1006.0268","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-06-01T23:55:18Z","cross_cats_sorted":["math.KT","math.RT"],"title_canon_sha256":"22bbfcbe7a530490bd8b20c4a73d4d06fa321731a277590ee68f333da415676b","abstract_canon_sha256":"e9c20747ae3d4e1a67fc4854e438733607b7d5431bfa0701999d310193223225"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:13.772148Z","signature_b64":"P+Hp56l63ZJOm+uaYxuYHg/2txj+txZagrUCByE8xyeGuxSpPEAL36V4bxmT1je/Y2JvMbRmM8ZxLxGpyypGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2772fa63f3d642626324994004f813a92730f6b48871f6666b57cf2f5122259e","last_reissued_at":"2026-05-18T04:02:13.771565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:13.771565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1006.0268","created_at":"2026-05-18T04:02:13.771656+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.0268v3","created_at":"2026-05-18T04:02:13.771656+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0268","created_at":"2026-05-18T04:02:13.771656+00:00"},{"alias_kind":"pith_short_12","alias_value":"E5ZPUY7T2ZBG","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"E5ZPUY7T2ZBGEYZE","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"E5ZPUY7T","created_at":"2026-05-18T12:26:06.534383+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E5ZPUY7T2ZBGEYZETFAAJ6ATVE","json":"https://pith.science/pith/E5ZPUY7T2ZBGEYZETFAAJ6ATVE.json","graph_json":"https://pith.science/api/pith-number/E5ZPUY7T2ZBGEYZETFAAJ6ATVE/graph.json","events_json":"https://pith.science/api/pith-number/E5ZPUY7T2ZBGEYZETFAAJ6ATVE/events.json","paper":"https://pith.science/paper/E5ZPUY7T"},"agent_actions":{"view_html":"https://pith.science/pith/E5ZPUY7T2ZBGEYZETFAAJ6ATVE","download_json":"https://pith.science/pith/E5ZPUY7T2ZBGEYZETFAAJ6ATVE.json","view_paper":"https://pith.science/paper/E5ZPUY7T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.0268&json=true","fetch_graph":"https://pith.science/api/pith-number/E5ZPUY7T2ZBGEYZETFAAJ6ATVE/graph.json","fetch_events":"https://pith.science/api/pith-number/E5ZPUY7T2ZBGEYZETFAAJ6ATVE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E5ZPUY7T2ZBGEYZETFAAJ6ATVE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E5ZPUY7T2ZBGEYZETFAAJ6ATVE/action/storage_attestation","attest_author":"https://pith.science/pith/E5ZPUY7T2ZBGEYZETFAAJ6ATVE/action/author_attestation","sign_citation":"https://pith.science/pith/E5ZPUY7T2ZBGEYZETFAAJ6ATVE/action/citation_signature","submit_replication":"https://pith.science/pith/E5ZPUY7T2ZBGEYZETFAAJ6ATVE/action/replication_record"}},"created_at":"2026-05-18T04:02:13.771656+00:00","updated_at":"2026-05-18T04:02:13.771656+00:00"}