{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4WVS3WACYISBKZR2XZMYGG53AW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3a117b4f4936a4dfcc767bfac133ecc8bb244856660f0e60f97be7c3f4cfba62","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-10-15T10:15:24Z","title_canon_sha256":"88ba4a5fa6781c521b1c56e981d219a211b48d4fb28f369f2e97c835904805c7"},"schema_version":"1.0","source":{"id":"1610.04710","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04710","created_at":"2026-05-18T00:51:43Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04710v2","created_at":"2026-05-18T00:51:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04710","created_at":"2026-05-18T00:51:43Z"},{"alias_kind":"pith_short_12","alias_value":"4WVS3WACYISB","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4WVS3WACYISBKZR2","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4WVS3WAC","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:03fbc9e8bbc31fc0646e448fd0c2ff43465dfcb939b9e8875499e997ba440b02","target":"graph","created_at":"2026-05-18T00:51:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 ","authors_text":"Alexandre Kosyak","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-10-15T10:15:24Z","title":"Criteria of irreducibility of the Koopman representations for the group ${\\rm GL}_0(2\\infty,{\\mathbb R})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04710","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:23bef0ac8e0782dc5aaa8df75373c49aa37f7135d9e54f60abce960d91d2b017","target":"record","created_at":"2026-05-18T00:51:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3a117b4f4936a4dfcc767bfac133ecc8bb244856660f0e60f97be7c3f4cfba62","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-10-15T10:15:24Z","title_canon_sha256":"88ba4a5fa6781c521b1c56e981d219a211b48d4fb28f369f2e97c835904805c7"},"schema_version":"1.0","source":{"id":"1610.04710","kind":"arxiv","version":2}},"canonical_sha256":"e5ab2dd802c22415663abe59831bbb05a2aa0f7080d93b5158d6cfe89a665b88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5ab2dd802c22415663abe59831bbb05a2aa0f7080d93b5158d6cfe89a665b88","first_computed_at":"2026-05-18T00:51:43.355683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:43.355683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HCgwpYIiVr2hAcEpRooS96LQunOJ/+O/Tin+0eWdWmTyOMe6rpcTPasydk/tkEqpDIegTsVXLrDRuCUt33u8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:43.356303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04710","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23bef0ac8e0782dc5aaa8df75373c49aa37f7135d9e54f60abce960d91d2b017","sha256:03fbc9e8bbc31fc0646e448fd0c2ff43465dfcb939b9e8875499e997ba440b02"],"state_sha256":"d050f1972719ecbab691e9bfceb7d841bef20fefa643ee7a52a17b6c8343f1e1"}