{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:IMFFCAA6WRNGLZVY6KMPHQOTEN","short_pith_number":"pith:IMFFCAA6","schema_version":"1.0","canonical_sha256":"430a51001eb45a65e6b8f298f3c1d32348e50db9c539c51019c100013a4d6d8f","source":{"kind":"arxiv","id":"1906.03468","version":1},"attestation_state":"computed","paper":{"title":"Weil representations via abstract data and Heisenberg groups: a comparison","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RA"],"primary_cat":"math.RT","authors_text":"Fernando Szechtman, James Cruickshank, Luis Guti\\'errez Frez","submitted_at":"2019-06-08T14:36:28Z","abstract_excerpt":"Let $B$ be a ring, not necessarily commutative, having an involution $*$ and let ${\\mathrm U}_{2m}(B)$ be the unitary group of rank $2m$ associated to a hermitian or skew hermitian form relative to $*$. When $B$ is finite, we construct a Weil representation of ${\\mathrm U}_{2m}(B)$ via Heisenberg groups and find its explicit matrix form on the Bruhat elements. As a consequence, we derive information on generalized Gauss sums. On the other hand, there is an axiomatic method to define a Weil representation of ${\\mathrm U}_{2m}(B)$, and we compare the two Weil representations thus obtained under "},"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":"1906.03468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-06-08T14:36:28Z","cross_cats_sorted":["math.GR","math.RA"],"title_canon_sha256":"42657dd8196d82fe37c457dd56f9fabeecfb7a5798e0c2a6dd34deea95f054ea","abstract_canon_sha256":"7fd0a6b9fbe8169c220fb3f071798acf056cba9dfda1acdc506c8a380df324b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:48.389898Z","signature_b64":"l0FYfn3wgTP15igjPMh/mE4T9SPAsWpcQ1rEi2URZU6UsfunGSXtUGZp0b7qZamCXjPLEZvoWg8GCiuBKZKqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"430a51001eb45a65e6b8f298f3c1d32348e50db9c539c51019c100013a4d6d8f","last_reissued_at":"2026-05-17T23:43:48.389182Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:48.389182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weil representations via abstract data and Heisenberg groups: a comparison","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RA"],"primary_cat":"math.RT","authors_text":"Fernando Szechtman, James Cruickshank, Luis Guti\\'errez Frez","submitted_at":"2019-06-08T14:36:28Z","abstract_excerpt":"Let $B$ be a ring, not necessarily commutative, having an involution $*$ and let ${\\mathrm U}_{2m}(B)$ be the unitary group of rank $2m$ associated to a hermitian or skew hermitian form relative to $*$. When $B$ is finite, we construct a Weil representation of ${\\mathrm U}_{2m}(B)$ via Heisenberg groups and find its explicit matrix form on the Bruhat elements. As a consequence, we derive information on generalized Gauss sums. On the other hand, there is an axiomatic method to define a Weil representation of ${\\mathrm U}_{2m}(B)$, and we compare the two Weil representations thus obtained under "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03468","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":"1906.03468","created_at":"2026-05-17T23:43:48.389279+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.03468v1","created_at":"2026-05-17T23:43:48.389279+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03468","created_at":"2026-05-17T23:43:48.389279+00:00"},{"alias_kind":"pith_short_12","alias_value":"IMFFCAA6WRNG","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"IMFFCAA6WRNGLZVY","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"IMFFCAA6","created_at":"2026-05-18T12:33:18.533446+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/IMFFCAA6WRNGLZVY6KMPHQOTEN","json":"https://pith.science/pith/IMFFCAA6WRNGLZVY6KMPHQOTEN.json","graph_json":"https://pith.science/api/pith-number/IMFFCAA6WRNGLZVY6KMPHQOTEN/graph.json","events_json":"https://pith.science/api/pith-number/IMFFCAA6WRNGLZVY6KMPHQOTEN/events.json","paper":"https://pith.science/paper/IMFFCAA6"},"agent_actions":{"view_html":"https://pith.science/pith/IMFFCAA6WRNGLZVY6KMPHQOTEN","download_json":"https://pith.science/pith/IMFFCAA6WRNGLZVY6KMPHQOTEN.json","view_paper":"https://pith.science/paper/IMFFCAA6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.03468&json=true","fetch_graph":"https://pith.science/api/pith-number/IMFFCAA6WRNGLZVY6KMPHQOTEN/graph.json","fetch_events":"https://pith.science/api/pith-number/IMFFCAA6WRNGLZVY6KMPHQOTEN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IMFFCAA6WRNGLZVY6KMPHQOTEN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IMFFCAA6WRNGLZVY6KMPHQOTEN/action/storage_attestation","attest_author":"https://pith.science/pith/IMFFCAA6WRNGLZVY6KMPHQOTEN/action/author_attestation","sign_citation":"https://pith.science/pith/IMFFCAA6WRNGLZVY6KMPHQOTEN/action/citation_signature","submit_replication":"https://pith.science/pith/IMFFCAA6WRNGLZVY6KMPHQOTEN/action/replication_record"}},"created_at":"2026-05-17T23:43:48.389279+00:00","updated_at":"2026-05-17T23:43:48.389279+00:00"}