{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XCFLVW3X2B4FDSKIUMKDMUPZY5","short_pith_number":"pith:XCFLVW3X","schema_version":"1.0","canonical_sha256":"b88abadb77d07851c948a3143651f9c768fbb83106cfabaf10bba7fb03ebf29e","source":{"kind":"arxiv","id":"1706.06240","version":2},"attestation_state":"computed","paper":{"title":"Spin nilHecke algebras of classical type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ian Johnson, Weiqiang Wang","submitted_at":"2017-06-20T02:18:43Z","abstract_excerpt":"We formulate and study the spin nilHecke algebras ${}^\\mathfrak{b}\\!{\\mathrm{NH}}_n^-$ and ${}^\\mathfrak{d}\\!{\\mathrm{NH}}_n^-$ of type B/D, which differ from the usual nilHecke algebras by some odd signs. The type B spin nilHecke algebra is a nil version of the spin type B Hecke algebra introduced earlier by the second author and Khongsap, but not for the type D one. We construct faithful polynomial representations $\\mathrm{Pol}_n^-$ of the nilHecke algebras via odd Demazure operators. We formulate the spin Schubert polynomials, and use them to show that the spin nilHecke algebras are matrix "},"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":"1706.06240","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-20T02:18:43Z","cross_cats_sorted":[],"title_canon_sha256":"6245dcb2527204e841dc9f00f25abbe9683595f86ceecf93040868ee72e2e9df","abstract_canon_sha256":"5589cb03ec048d218e98fbb08c5da4875be7edda2ecb3e21588d5910f9c7f1b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:52.376220Z","signature_b64":"S5oL4NzeKjQ3GExACT8bkiGquMrQppZM2luHBSgJWeYebRDU0yi9QKvyunpQ1U7h3FMoh2Hs2MkVWBom0BBtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b88abadb77d07851c948a3143651f9c768fbb83106cfabaf10bba7fb03ebf29e","last_reissued_at":"2026-05-18T00:24:52.375721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:52.375721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spin nilHecke algebras of classical type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ian Johnson, Weiqiang Wang","submitted_at":"2017-06-20T02:18:43Z","abstract_excerpt":"We formulate and study the spin nilHecke algebras ${}^\\mathfrak{b}\\!{\\mathrm{NH}}_n^-$ and ${}^\\mathfrak{d}\\!{\\mathrm{NH}}_n^-$ of type B/D, which differ from the usual nilHecke algebras by some odd signs. The type B spin nilHecke algebra is a nil version of the spin type B Hecke algebra introduced earlier by the second author and Khongsap, but not for the type D one. We construct faithful polynomial representations $\\mathrm{Pol}_n^-$ of the nilHecke algebras via odd Demazure operators. We formulate the spin Schubert polynomials, and use them to show that the spin nilHecke algebras are matrix "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06240","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":"1706.06240","created_at":"2026-05-18T00:24:52.375805+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.06240v2","created_at":"2026-05-18T00:24:52.375805+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06240","created_at":"2026-05-18T00:24:52.375805+00:00"},{"alias_kind":"pith_short_12","alias_value":"XCFLVW3X2B4F","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"XCFLVW3X2B4FDSKI","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"XCFLVW3X","created_at":"2026-05-18T12:31:53.515858+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/XCFLVW3X2B4FDSKIUMKDMUPZY5","json":"https://pith.science/pith/XCFLVW3X2B4FDSKIUMKDMUPZY5.json","graph_json":"https://pith.science/api/pith-number/XCFLVW3X2B4FDSKIUMKDMUPZY5/graph.json","events_json":"https://pith.science/api/pith-number/XCFLVW3X2B4FDSKIUMKDMUPZY5/events.json","paper":"https://pith.science/paper/XCFLVW3X"},"agent_actions":{"view_html":"https://pith.science/pith/XCFLVW3X2B4FDSKIUMKDMUPZY5","download_json":"https://pith.science/pith/XCFLVW3X2B4FDSKIUMKDMUPZY5.json","view_paper":"https://pith.science/paper/XCFLVW3X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.06240&json=true","fetch_graph":"https://pith.science/api/pith-number/XCFLVW3X2B4FDSKIUMKDMUPZY5/graph.json","fetch_events":"https://pith.science/api/pith-number/XCFLVW3X2B4FDSKIUMKDMUPZY5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XCFLVW3X2B4FDSKIUMKDMUPZY5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XCFLVW3X2B4FDSKIUMKDMUPZY5/action/storage_attestation","attest_author":"https://pith.science/pith/XCFLVW3X2B4FDSKIUMKDMUPZY5/action/author_attestation","sign_citation":"https://pith.science/pith/XCFLVW3X2B4FDSKIUMKDMUPZY5/action/citation_signature","submit_replication":"https://pith.science/pith/XCFLVW3X2B4FDSKIUMKDMUPZY5/action/replication_record"}},"created_at":"2026-05-18T00:24:52.375805+00:00","updated_at":"2026-05-18T00:24:52.375805+00:00"}