{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:HQQDHPZOD2LPNDLHEZHNAP6IKM","short_pith_number":"pith:HQQDHPZO","schema_version":"1.0","canonical_sha256":"3c2033bf2e1e96f68d67264ed03fc85325e286175d3698e816b7d84036db76f7","source":{"kind":"arxiv","id":"1102.0310","version":3},"attestation_state":"computed","paper":{"title":"Highest weight vectors for the adjoint action of GL_n on polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Rudolf Tange","submitted_at":"2011-02-01T22:12:26Z","abstract_excerpt":"Let G=GL_n be the general linear group over an algebraically closed field k and let g=gl_n be its Lie algebra. Let U be the subgroup of G which consists of the upper unitriangular matrices. Let k[g] be the algebra of regular functions on $\\g$. For 2(n-1)-1 weights we give explicit bases for the k[g]^G-module k[g]^U_\\lambda of highest weight vectors of weight \\lambda. For 5 of those weights we show that this basis is algebraically independent over the invariants k[g]^G and generates the k[g]^G-algebra $\\bigoplus_{r\\ge0}k[\\g]^U_{r\\lambda}$. Finally we formulate a question which asks whether in c"},"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":"1102.0310","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-01T22:12:26Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"0ceb0f6d1e8ba2506099dd47459a5fbba2b98da471fcb7b5619140bf8d933aeb","abstract_canon_sha256":"6ba56aa790a71548a957b430e891bb8d20d3f593365e9ab0e40cebbea1467c7b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:23.790478Z","signature_b64":"bB7ykaVZqjaEpVjWqyf5FHMT6c6ipW1pwwN+7dna8riQ9KMgDDidB3SsKhEXVHik1/1TGfYTK85dJ0voOY71DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c2033bf2e1e96f68d67264ed03fc85325e286175d3698e816b7d84036db76f7","last_reissued_at":"2026-05-18T04:01:23.789817Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:23.789817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Highest weight vectors for the adjoint action of GL_n on polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Rudolf Tange","submitted_at":"2011-02-01T22:12:26Z","abstract_excerpt":"Let G=GL_n be the general linear group over an algebraically closed field k and let g=gl_n be its Lie algebra. Let U be the subgroup of G which consists of the upper unitriangular matrices. Let k[g] be the algebra of regular functions on $\\g$. For 2(n-1)-1 weights we give explicit bases for the k[g]^G-module k[g]^U_\\lambda of highest weight vectors of weight \\lambda. For 5 of those weights we show that this basis is algebraically independent over the invariants k[g]^G and generates the k[g]^G-algebra $\\bigoplus_{r\\ge0}k[\\g]^U_{r\\lambda}$. Finally we formulate a question which asks whether in c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0310","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":"1102.0310","created_at":"2026-05-18T04:01:23.789915+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.0310v3","created_at":"2026-05-18T04:01:23.789915+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0310","created_at":"2026-05-18T04:01:23.789915+00:00"},{"alias_kind":"pith_short_12","alias_value":"HQQDHPZOD2LP","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"HQQDHPZOD2LPNDLH","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"HQQDHPZO","created_at":"2026-05-18T12:26:30.835961+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/HQQDHPZOD2LPNDLHEZHNAP6IKM","json":"https://pith.science/pith/HQQDHPZOD2LPNDLHEZHNAP6IKM.json","graph_json":"https://pith.science/api/pith-number/HQQDHPZOD2LPNDLHEZHNAP6IKM/graph.json","events_json":"https://pith.science/api/pith-number/HQQDHPZOD2LPNDLHEZHNAP6IKM/events.json","paper":"https://pith.science/paper/HQQDHPZO"},"agent_actions":{"view_html":"https://pith.science/pith/HQQDHPZOD2LPNDLHEZHNAP6IKM","download_json":"https://pith.science/pith/HQQDHPZOD2LPNDLHEZHNAP6IKM.json","view_paper":"https://pith.science/paper/HQQDHPZO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.0310&json=true","fetch_graph":"https://pith.science/api/pith-number/HQQDHPZOD2LPNDLHEZHNAP6IKM/graph.json","fetch_events":"https://pith.science/api/pith-number/HQQDHPZOD2LPNDLHEZHNAP6IKM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HQQDHPZOD2LPNDLHEZHNAP6IKM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HQQDHPZOD2LPNDLHEZHNAP6IKM/action/storage_attestation","attest_author":"https://pith.science/pith/HQQDHPZOD2LPNDLHEZHNAP6IKM/action/author_attestation","sign_citation":"https://pith.science/pith/HQQDHPZOD2LPNDLHEZHNAP6IKM/action/citation_signature","submit_replication":"https://pith.science/pith/HQQDHPZOD2LPNDLHEZHNAP6IKM/action/replication_record"}},"created_at":"2026-05-18T04:01:23.789915+00:00","updated_at":"2026-05-18T04:01:23.789915+00:00"}