{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:KKUY3R3Y42WU2ON4ZM2XEED6WW","short_pith_number":"pith:KKUY3R3Y","schema_version":"1.0","canonical_sha256":"52a98dc778e6ad4d39bccb3572107eb5950596cc254b72cf9da175bc41c48643","source":{"kind":"arxiv","id":"1808.05251","version":1},"attestation_state":"computed","paper":{"title":"A positive-definite inner product for vector-valued 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":"2018-08-15T18:55:50Z","abstract_excerpt":"In a previous paper J.-G. Luque and the author (Sem. Loth. Combin. 2011) developed the theory of nonsymmetric Macdonald polynomials taking values in an irreducible module of the Hecke algebra of the symmetric group $\\mathcal{S}_{N}$. The polynomials are parametrized by $\\left( q,t\\right) $ and are simultaneous eigenfunctions of a commuting set of Cherednik operators, which were studied by Baker and Forrester (IMRN 1997). In the Dunkl-Luque paper there is a construction of a pairing between $\\left( q^{-1},t^{-1}\\right) $ polynomials and $\\left( q,t\\right) $ polynomials, and for which the Macdon"},"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":"1808.05251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-08-15T18:55:50Z","cross_cats_sorted":[],"title_canon_sha256":"5eb18cd3659b1b7f1912651401370b1ccde12fe7e7820a7379e839ca148a0109","abstract_canon_sha256":"25b19d0ae2c90a80793bc084713d3c0d09faf2313060a182a13b3c6596b018c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:03.371930Z","signature_b64":"n1yQZI6Q3z+DWxr/tkSTOylWATAbAfmja2ACFMVhlEeh0H6qNkJ5d0p+/yGeQNXDB0jdqkmN67PPB7r82mHhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52a98dc778e6ad4d39bccb3572107eb5950596cc254b72cf9da175bc41c48643","last_reissued_at":"2026-05-17T23:55:03.371536Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:03.371536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A positive-definite inner product for vector-valued 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":"2018-08-15T18:55:50Z","abstract_excerpt":"In a previous paper J.-G. Luque and the author (Sem. Loth. Combin. 2011) developed the theory of nonsymmetric Macdonald polynomials taking values in an irreducible module of the Hecke algebra of the symmetric group $\\mathcal{S}_{N}$. The polynomials are parametrized by $\\left( q,t\\right) $ and are simultaneous eigenfunctions of a commuting set of Cherednik operators, which were studied by Baker and Forrester (IMRN 1997). In the Dunkl-Luque paper there is a construction of a pairing between $\\left( q^{-1},t^{-1}\\right) $ polynomials and $\\left( q,t\\right) $ polynomials, and for which the Macdon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05251","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":"1808.05251","created_at":"2026-05-17T23:55:03.371599+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.05251v1","created_at":"2026-05-17T23:55:03.371599+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05251","created_at":"2026-05-17T23:55:03.371599+00:00"},{"alias_kind":"pith_short_12","alias_value":"KKUY3R3Y42WU","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"KKUY3R3Y42WU2ON4","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"KKUY3R3Y","created_at":"2026-05-18T12:32:33.847187+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/KKUY3R3Y42WU2ON4ZM2XEED6WW","json":"https://pith.science/pith/KKUY3R3Y42WU2ON4ZM2XEED6WW.json","graph_json":"https://pith.science/api/pith-number/KKUY3R3Y42WU2ON4ZM2XEED6WW/graph.json","events_json":"https://pith.science/api/pith-number/KKUY3R3Y42WU2ON4ZM2XEED6WW/events.json","paper":"https://pith.science/paper/KKUY3R3Y"},"agent_actions":{"view_html":"https://pith.science/pith/KKUY3R3Y42WU2ON4ZM2XEED6WW","download_json":"https://pith.science/pith/KKUY3R3Y42WU2ON4ZM2XEED6WW.json","view_paper":"https://pith.science/paper/KKUY3R3Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.05251&json=true","fetch_graph":"https://pith.science/api/pith-number/KKUY3R3Y42WU2ON4ZM2XEED6WW/graph.json","fetch_events":"https://pith.science/api/pith-number/KKUY3R3Y42WU2ON4ZM2XEED6WW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KKUY3R3Y42WU2ON4ZM2XEED6WW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KKUY3R3Y42WU2ON4ZM2XEED6WW/action/storage_attestation","attest_author":"https://pith.science/pith/KKUY3R3Y42WU2ON4ZM2XEED6WW/action/author_attestation","sign_citation":"https://pith.science/pith/KKUY3R3Y42WU2ON4ZM2XEED6WW/action/citation_signature","submit_replication":"https://pith.science/pith/KKUY3R3Y42WU2ON4ZM2XEED6WW/action/replication_record"}},"created_at":"2026-05-17T23:55:03.371599+00:00","updated_at":"2026-05-17T23:55:03.371599+00:00"}