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We describe the structure of these sequences in case the dimension $n$ is odd. It follows from the construction that all these operators are invariant with respect to the action of the group $G$.\n  These results are obtained by"},"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":"0710.0093","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-09-29T20:16:27Z","cross_cats_sorted":[],"title_canon_sha256":"494bf083172067d2fe80cdadc68ed395e0de8a73d029b6063801ebe209d87c2d","abstract_canon_sha256":"3e695ccdff562c970e98a2a459d8dff95b431a17dbef8df22c26180b24cce873"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:14.306814Z","signature_b64":"rTVNYYx/nmNV0w0BouMnnB+0Zk8m9fM/ejpg8puc7eTz4c0Zi+MWhYz7YBKC6+Km0/mRLC80EfMJc9e8+DiwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acaa7feb4c90b326db4610608ff9d8c91f64e412d0f8d969fb639b60aeca1b70","last_reissued_at":"2026-05-18T04:09:14.306302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:14.306302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Dolbeault sequences in parabolic geometry","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Peter Franek","submitted_at":"2007-09-29T20:16:27Z","abstract_excerpt":"In this paper, we show the existence of a sequence of invariant differential operators on a particular homogeneous model $G/P$ of a Cartan geometry. 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It follows from the construction that all these operators are invariant with respect to the action of the group $G$.\n  These results are obtained by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.0093","kind":"arxiv","version":2},"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":"0710.0093","created_at":"2026-05-18T04:09:14.306388+00:00"},{"alias_kind":"arxiv_version","alias_value":"0710.0093v2","created_at":"2026-05-18T04:09:14.306388+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.0093","created_at":"2026-05-18T04:09:14.306388+00:00"},{"alias_kind":"pith_short_12","alias_value":"VSVH722MSCZS","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"VSVH722MSCZSNW2G","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"VSVH722M","created_at":"2026-05-18T12:25:56.245647+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/VSVH722MSCZSNW2GCBQI76OYZE","json":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE.json","graph_json":"https://pith.science/api/pith-number/VSVH722MSCZSNW2GCBQI76OYZE/graph.json","events_json":"https://pith.science/api/pith-number/VSVH722MSCZSNW2GCBQI76OYZE/events.json","paper":"https://pith.science/paper/VSVH722M"},"agent_actions":{"view_html":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE","download_json":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE.json","view_paper":"https://pith.science/paper/VSVH722M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0710.0093&json=true","fetch_graph":"https://pith.science/api/pith-number/VSVH722MSCZSNW2GCBQI76OYZE/graph.json","fetch_events":"https://pith.science/api/pith-number/VSVH722MSCZSNW2GCBQI76OYZE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE/action/storage_attestation","attest_author":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE/action/author_attestation","sign_citation":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE/action/citation_signature","submit_replication":"https://pith.science/pith/VSVH722MSCZSNW2GCBQI76OYZE/action/replication_record"}},"created_at":"2026-05-18T04:09:14.306388+00:00","updated_at":"2026-05-18T04:09:14.306388+00:00"}