{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:3EQNFIWVGTI2BEFNTFIGSGZ3NT","short_pith_number":"pith:3EQNFIWV","schema_version":"1.0","canonical_sha256":"d920d2a2d534d1a090ad9950691b3b6ccbd80639c6bbc6a1219fbc606a2367b3","source":{"kind":"arxiv","id":"1902.02310","version":1},"attestation_state":"computed","paper":{"title":"Some Singular Vector-valued Jack and Macdonald Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Charles F. Dunkl","submitted_at":"2019-02-06T18:07:38Z","abstract_excerpt":"For each partition $\\tau$ of $N$ there are irreducible modules of the symmetric groups $\\mathcal{S}_{N}$ or the corresponding Hecke algebra $\\mathcal{H}_{N}\\left( t\\right) $ whose bases consist of reverse standard Young tableaux of shape $\\tau$. There are associated spaces of nonsymmetric Jack and Macdonald polynomials taking values in these modules, respectively.The Jack polynomials are a special case of those constructed by Griffeth for the infinite family $G\\left( n,p,N\\right) $ of complex reflection groups. The Macdonald polynomials were constructed by Luque and the author. For both the gr"},"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":"1902.02310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-06T18:07:38Z","cross_cats_sorted":[],"title_canon_sha256":"7b7bf786eeff865486aa5ea9bc01c579f2fea621a2ca7f1b1fb575928e008383","abstract_canon_sha256":"0c5bce946dc57fd2bc848ce30cb28b809528d07449cff07e3a5fd56e0a6d0ed9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:37.363311Z","signature_b64":"PgCLcpMZaDpKTWeCu1C7LjwlylcKnR64OjuyAltZHuiMHnDRvRB4sCFMpKbS5pJeWJqbWigPoj4ZkWGLZK3WCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d920d2a2d534d1a090ad9950691b3b6ccbd80639c6bbc6a1219fbc606a2367b3","last_reissued_at":"2026-05-17T23:54:37.362586Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:37.362586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Singular Vector-valued Jack and Macdonald Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Charles F. Dunkl","submitted_at":"2019-02-06T18:07:38Z","abstract_excerpt":"For each partition $\\tau$ of $N$ there are irreducible modules of the symmetric groups $\\mathcal{S}_{N}$ or the corresponding Hecke algebra $\\mathcal{H}_{N}\\left( t\\right) $ whose bases consist of reverse standard Young tableaux of shape $\\tau$. There are associated spaces of nonsymmetric Jack and Macdonald polynomials taking values in these modules, respectively.The Jack polynomials are a special case of those constructed by Griffeth for the infinite family $G\\left( n,p,N\\right) $ of complex reflection groups. The Macdonald polynomials were constructed by Luque and the author. For both the gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02310","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1902.02310","created_at":"2026-05-17T23:54:37.362715+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.02310v1","created_at":"2026-05-17T23:54:37.362715+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02310","created_at":"2026-05-17T23:54:37.362715+00:00"},{"alias_kind":"pith_short_12","alias_value":"3EQNFIWVGTI2","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"3EQNFIWVGTI2BEFN","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"3EQNFIWV","created_at":"2026-05-18T12:33:07.085635+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/3EQNFIWVGTI2BEFNTFIGSGZ3NT","json":"https://pith.science/pith/3EQNFIWVGTI2BEFNTFIGSGZ3NT.json","graph_json":"https://pith.science/api/pith-number/3EQNFIWVGTI2BEFNTFIGSGZ3NT/graph.json","events_json":"https://pith.science/api/pith-number/3EQNFIWVGTI2BEFNTFIGSGZ3NT/events.json","paper":"https://pith.science/paper/3EQNFIWV"},"agent_actions":{"view_html":"https://pith.science/pith/3EQNFIWVGTI2BEFNTFIGSGZ3NT","download_json":"https://pith.science/pith/3EQNFIWVGTI2BEFNTFIGSGZ3NT.json","view_paper":"https://pith.science/paper/3EQNFIWV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.02310&json=true","fetch_graph":"https://pith.science/api/pith-number/3EQNFIWVGTI2BEFNTFIGSGZ3NT/graph.json","fetch_events":"https://pith.science/api/pith-number/3EQNFIWVGTI2BEFNTFIGSGZ3NT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3EQNFIWVGTI2BEFNTFIGSGZ3NT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3EQNFIWVGTI2BEFNTFIGSGZ3NT/action/storage_attestation","attest_author":"https://pith.science/pith/3EQNFIWVGTI2BEFNTFIGSGZ3NT/action/author_attestation","sign_citation":"https://pith.science/pith/3EQNFIWVGTI2BEFNTFIGSGZ3NT/action/citation_signature","submit_replication":"https://pith.science/pith/3EQNFIWVGTI2BEFNTFIGSGZ3NT/action/replication_record"}},"created_at":"2026-05-17T23:54:37.362715+00:00","updated_at":"2026-05-17T23:54:37.362715+00:00"}