{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QHYSRII7HOXXYBES3KV6UGSKQB","short_pith_number":"pith:QHYSRII7","schema_version":"1.0","canonical_sha256":"81f128a11f3baf7c0492daabea1a4a806bfdd49c906435803e849a2a37427e28","source":{"kind":"arxiv","id":"1506.08071","version":2},"attestation_state":"computed","paper":{"title":"Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jos\\'e Pantoja, Luis Guti\\'errez Frez","submitted_at":"2015-06-26T13:38:34Z","abstract_excerpt":"We construct a complex linear Weil representation $\\rho$ of the generalized special linear group $G={\\rm SL}_*^{1}(2,A_n)$ ($A_n=K[x]/\\langle x^n\\rangle$, $K$ the quadratic extension of the finite field $k$ of $q$ elements, $q$ odd), where $A_n$ is endowed with a second class involution. After the construction of a specific data, the representation is defined on the generators of a Bruhat presentation of $G$, via linear operators satisfying the relations of the presentation. The structure of a unitary group $U$ associated to $G$ is described. Using this group we obtain a first decomposition of"},"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":"1506.08071","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.RT","submitted_at":"2015-06-26T13:38:34Z","cross_cats_sorted":[],"title_canon_sha256":"d71b6a6ca8b620d7bcae100c197fb7675e361def2dd07278dbe28ae1ef033f51","abstract_canon_sha256":"badabbec46605e753f6ea91f5259b77760257f2f2d180179bf0a8a52f86b238f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:00.280889Z","signature_b64":"WlmBkWRC35VelooKPGvxkTCwQiAwOEb/qL2frtN/OcstbfwWgAhssBFLSKiPyymLjOiOD2vot70QRzGS6fRJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81f128a11f3baf7c0492daabea1a4a806bfdd49c906435803e849a2a37427e28","last_reissued_at":"2026-05-18T01:32:00.280279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:00.280279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jos\\'e Pantoja, Luis Guti\\'errez Frez","submitted_at":"2015-06-26T13:38:34Z","abstract_excerpt":"We construct a complex linear Weil representation $\\rho$ of the generalized special linear group $G={\\rm SL}_*^{1}(2,A_n)$ ($A_n=K[x]/\\langle x^n\\rangle$, $K$ the quadratic extension of the finite field $k$ of $q$ elements, $q$ odd), where $A_n$ is endowed with a second class involution. After the construction of a specific data, the representation is defined on the generators of a Bruhat presentation of $G$, via linear operators satisfying the relations of the presentation. The structure of a unitary group $U$ associated to $G$ is described. Using this group we obtain a first decomposition of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08071","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":"1506.08071","created_at":"2026-05-18T01:32:00.280375+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.08071v2","created_at":"2026-05-18T01:32:00.280375+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08071","created_at":"2026-05-18T01:32:00.280375+00:00"},{"alias_kind":"pith_short_12","alias_value":"QHYSRII7HOXX","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"QHYSRII7HOXXYBES","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"QHYSRII7","created_at":"2026-05-18T12:29:37.295048+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/QHYSRII7HOXXYBES3KV6UGSKQB","json":"https://pith.science/pith/QHYSRII7HOXXYBES3KV6UGSKQB.json","graph_json":"https://pith.science/api/pith-number/QHYSRII7HOXXYBES3KV6UGSKQB/graph.json","events_json":"https://pith.science/api/pith-number/QHYSRII7HOXXYBES3KV6UGSKQB/events.json","paper":"https://pith.science/paper/QHYSRII7"},"agent_actions":{"view_html":"https://pith.science/pith/QHYSRII7HOXXYBES3KV6UGSKQB","download_json":"https://pith.science/pith/QHYSRII7HOXXYBES3KV6UGSKQB.json","view_paper":"https://pith.science/paper/QHYSRII7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.08071&json=true","fetch_graph":"https://pith.science/api/pith-number/QHYSRII7HOXXYBES3KV6UGSKQB/graph.json","fetch_events":"https://pith.science/api/pith-number/QHYSRII7HOXXYBES3KV6UGSKQB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QHYSRII7HOXXYBES3KV6UGSKQB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QHYSRII7HOXXYBES3KV6UGSKQB/action/storage_attestation","attest_author":"https://pith.science/pith/QHYSRII7HOXXYBES3KV6UGSKQB/action/author_attestation","sign_citation":"https://pith.science/pith/QHYSRII7HOXXYBES3KV6UGSKQB/action/citation_signature","submit_replication":"https://pith.science/pith/QHYSRII7HOXXYBES3KV6UGSKQB/action/replication_record"}},"created_at":"2026-05-18T01:32:00.280375+00:00","updated_at":"2026-05-18T01:32:00.280375+00:00"}