{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AMMARBUY34QKW5F3GNCNACTBLM","short_pith_number":"pith:AMMARBUY","schema_version":"1.0","canonical_sha256":"0318088698df20ab74bb3344d00a615b2ec13ac324eee1796a5e59199a994245","source":{"kind":"arxiv","id":"1507.07410","version":2},"attestation_state":"computed","paper":{"title":"Irreducible representations of unipotent subgroups of symplectic and unitary groups defined over rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fernando Szechtman","submitted_at":"2015-07-27T14:17:41Z","abstract_excerpt":"Let $A$ be a ring with $1\\neq 0$, not necessarily finite, endowed with an involution~$*$, that is, an anti-automorphism of order $\\leq 2$. Let $H_n(A)$ be the additive group of all $n\\times n$ hermitian matrices over $A$ relative to $*$. Let ${\\mathcal U}_n(A)$ be the subgroup of $\\mathrm{GL}_n(A)$ of all upper triangular matrices with 1's along the main diagonal. Let $P=H_n(A)\\rtimes {\\mathcal U}_n(A)$, where ${\\mathcal U}_n(A)$ acts on $H_n(A)$ by $*$-congruence transformations. We may view $P$ as a unipotent subgroup of either a symplectic group $\\mathrm{Sp}_{2n}(A)$, if $*=1_A$ (in which c"},"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":"1507.07410","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-27T14:17:41Z","cross_cats_sorted":[],"title_canon_sha256":"2f5d5d7ff2e207b5525dd2df1dc8e92ab843a7dcacc81b337362deffcef369ad","abstract_canon_sha256":"c5108552edf85d8ba5dd08027308b8adea51057f2ee779a4f6e2c9e8df5e4662"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:46.236389Z","signature_b64":"/z9/e6Hp/6MT0TAv5ZZRuCM5A3fn+ijfU4BUFCrzkcn7cYUTaW3iJ1E+QEIXRuY0HPThcpgq5TeBpTnxp3bIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0318088698df20ab74bb3344d00a615b2ec13ac324eee1796a5e59199a994245","last_reissued_at":"2026-05-18T01:00:46.236005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:46.236005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Irreducible representations of unipotent subgroups of symplectic and unitary groups defined over rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fernando Szechtman","submitted_at":"2015-07-27T14:17:41Z","abstract_excerpt":"Let $A$ be a ring with $1\\neq 0$, not necessarily finite, endowed with an involution~$*$, that is, an anti-automorphism of order $\\leq 2$. Let $H_n(A)$ be the additive group of all $n\\times n$ hermitian matrices over $A$ relative to $*$. Let ${\\mathcal U}_n(A)$ be the subgroup of $\\mathrm{GL}_n(A)$ of all upper triangular matrices with 1's along the main diagonal. Let $P=H_n(A)\\rtimes {\\mathcal U}_n(A)$, where ${\\mathcal U}_n(A)$ acts on $H_n(A)$ by $*$-congruence transformations. We may view $P$ as a unipotent subgroup of either a symplectic group $\\mathrm{Sp}_{2n}(A)$, if $*=1_A$ (in which c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07410","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":"1507.07410","created_at":"2026-05-18T01:00:46.236064+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.07410v2","created_at":"2026-05-18T01:00:46.236064+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07410","created_at":"2026-05-18T01:00:46.236064+00:00"},{"alias_kind":"pith_short_12","alias_value":"AMMARBUY34QK","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AMMARBUY34QKW5F3","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AMMARBUY","created_at":"2026-05-18T12:29:10.953037+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/AMMARBUY34QKW5F3GNCNACTBLM","json":"https://pith.science/pith/AMMARBUY34QKW5F3GNCNACTBLM.json","graph_json":"https://pith.science/api/pith-number/AMMARBUY34QKW5F3GNCNACTBLM/graph.json","events_json":"https://pith.science/api/pith-number/AMMARBUY34QKW5F3GNCNACTBLM/events.json","paper":"https://pith.science/paper/AMMARBUY"},"agent_actions":{"view_html":"https://pith.science/pith/AMMARBUY34QKW5F3GNCNACTBLM","download_json":"https://pith.science/pith/AMMARBUY34QKW5F3GNCNACTBLM.json","view_paper":"https://pith.science/paper/AMMARBUY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.07410&json=true","fetch_graph":"https://pith.science/api/pith-number/AMMARBUY34QKW5F3GNCNACTBLM/graph.json","fetch_events":"https://pith.science/api/pith-number/AMMARBUY34QKW5F3GNCNACTBLM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AMMARBUY34QKW5F3GNCNACTBLM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AMMARBUY34QKW5F3GNCNACTBLM/action/storage_attestation","attest_author":"https://pith.science/pith/AMMARBUY34QKW5F3GNCNACTBLM/action/author_attestation","sign_citation":"https://pith.science/pith/AMMARBUY34QKW5F3GNCNACTBLM/action/citation_signature","submit_replication":"https://pith.science/pith/AMMARBUY34QKW5F3GNCNACTBLM/action/replication_record"}},"created_at":"2026-05-18T01:00:46.236064+00:00","updated_at":"2026-05-18T01:00:46.236064+00:00"}