{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4WVS3WACYISBKZR2XZMYGG53AW","short_pith_number":"pith:4WVS3WAC","schema_version":"1.0","canonical_sha256":"e5ab2dd802c22415663abe59831bbb05a2aa0f7080d93b5158d6cfe89a665b88","source":{"kind":"arxiv","id":"1610.04710","version":2},"attestation_state":"computed","paper":{"title":"Criteria of irreducibility of the Koopman representations for the group ${\\rm GL}_0(2\\infty,{\\mathbb R})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Alexandre Kosyak","submitted_at":"2016-10-15T10:15:24Z","abstract_excerpt":"Our aim is to find the irreducibility criteria for the Koopman representation, when the group acts on some space with a measure (Conjecture 1.5). Some general necessary conditions of the irreducibility of this representation are established. In the particular case of the group ${\\rm GL}_0(2\\infty,{\\mathbb R})$ $= \\varinjlim_{n}{\\rm GL}(2n-1,{\\mathbb R})$, the inductive limit of the general linear groups we prove that these conditions are also the necessary ones. The corresponding measure is infinite tensor products of one-dimensional arbitrary Gaussian non-centered measures. The corresponding "},"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":"1610.04710","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-10-15T10:15:24Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"88ba4a5fa6781c521b1c56e981d219a211b48d4fb28f369f2e97c835904805c7","abstract_canon_sha256":"3a117b4f4936a4dfcc767bfac133ecc8bb244856660f0e60f97be7c3f4cfba62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:43.356303Z","signature_b64":"HCgwpYIiVr2hAcEpRooS96LQunOJ/+O/Tin+0eWdWmTyOMe6rpcTPasydk/tkEqpDIegTsVXLrDRuCUt33u8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5ab2dd802c22415663abe59831bbb05a2aa0f7080d93b5158d6cfe89a665b88","last_reissued_at":"2026-05-18T00:51:43.355683Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:43.355683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Criteria of irreducibility of the Koopman representations for the group ${\\rm GL}_0(2\\infty,{\\mathbb R})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Alexandre Kosyak","submitted_at":"2016-10-15T10:15:24Z","abstract_excerpt":"Our aim is to find the irreducibility criteria for the Koopman representation, when the group acts on some space with a measure (Conjecture 1.5). Some general necessary conditions of the irreducibility of this representation are established. In the particular case of the group ${\\rm GL}_0(2\\infty,{\\mathbb R})$ $= \\varinjlim_{n}{\\rm GL}(2n-1,{\\mathbb R})$, the inductive limit of the general linear groups we prove that these conditions are also the necessary ones. The corresponding measure is infinite tensor products of one-dimensional arbitrary Gaussian non-centered measures. The corresponding "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04710","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":"1610.04710","created_at":"2026-05-18T00:51:43.355762+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.04710v2","created_at":"2026-05-18T00:51:43.355762+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04710","created_at":"2026-05-18T00:51:43.355762+00:00"},{"alias_kind":"pith_short_12","alias_value":"4WVS3WACYISB","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4WVS3WACYISBKZR2","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4WVS3WAC","created_at":"2026-05-18T12:29:58.707656+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/4WVS3WACYISBKZR2XZMYGG53AW","json":"https://pith.science/pith/4WVS3WACYISBKZR2XZMYGG53AW.json","graph_json":"https://pith.science/api/pith-number/4WVS3WACYISBKZR2XZMYGG53AW/graph.json","events_json":"https://pith.science/api/pith-number/4WVS3WACYISBKZR2XZMYGG53AW/events.json","paper":"https://pith.science/paper/4WVS3WAC"},"agent_actions":{"view_html":"https://pith.science/pith/4WVS3WACYISBKZR2XZMYGG53AW","download_json":"https://pith.science/pith/4WVS3WACYISBKZR2XZMYGG53AW.json","view_paper":"https://pith.science/paper/4WVS3WAC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.04710&json=true","fetch_graph":"https://pith.science/api/pith-number/4WVS3WACYISBKZR2XZMYGG53AW/graph.json","fetch_events":"https://pith.science/api/pith-number/4WVS3WACYISBKZR2XZMYGG53AW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4WVS3WACYISBKZR2XZMYGG53AW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4WVS3WACYISBKZR2XZMYGG53AW/action/storage_attestation","attest_author":"https://pith.science/pith/4WVS3WACYISBKZR2XZMYGG53AW/action/author_attestation","sign_citation":"https://pith.science/pith/4WVS3WACYISBKZR2XZMYGG53AW/action/citation_signature","submit_replication":"https://pith.science/pith/4WVS3WACYISBKZR2XZMYGG53AW/action/replication_record"}},"created_at":"2026-05-18T00:51:43.355762+00:00","updated_at":"2026-05-18T00:51:43.355762+00:00"}