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We prove that the Hamiltonian flows of all minors are complete. As a corollary we obtain that all Kogan-Zelevinsky integrable systems on M_{n,n} are complete and thus induce (analytic) Hamiltonian actions of C^{n(n-1)/2} on (M_{n,n}, pi_{n,n}) (as well as on GL_n(C) and on SL_n(C)).\n  We define Gelfand-Zeitlin integrable systems on (M_{n,n}, pi_{n,n}) from chains ","authors_text":"Michael Gekhtman, Milen Yakimov","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-09-26T14:57:19Z","title":"Completeness of determinantal Hamiltonian flows on the matrix affine Poisson space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4650","kind":"arxiv","version":1},"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:c28c979be6ee5dc37e8b467d4903881816440098234ab098dc642e33c76ced15","target":"record","created_at":"2026-05-18T02:15:33Z","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":"bdbc5317340abc69b2ae8f74ba8798723215246c7767c13aae5d20a2723727d6","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-09-26T14:57:19Z","title_canon_sha256":"6ea9f96da5c8d253f839ef430299e4bb487b3912a76271afd1e968f389bf459f"},"schema_version":"1.0","source":{"id":"0809.4650","kind":"arxiv","version":1}},"canonical_sha256":"f5668e5b8fa0a9adc9cf30a2e5b2cee5959ab5164155359931c7b7e2b73a6733","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5668e5b8fa0a9adc9cf30a2e5b2cee5959ab5164155359931c7b7e2b73a6733","first_computed_at":"2026-05-18T02:15:33.446234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:33.446234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7JRHfyoDnPJCUtd0HsWByUq4u9EIFdO3k4SWbUb/QTlaSgJsyTkMHvsv8UgTU5m2UpD99WhFuHXaIjWVMyESCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:33.446897Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.4650","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c28c979be6ee5dc37e8b467d4903881816440098234ab098dc642e33c76ced15","sha256:ec60ef4e6db4edf92e85ad02f79ded373c2b9b7547dcf3bd8313f4e73c7821f9"],"state_sha256":"9ddbf3c30245fda449025f2f646e091db09c0966843c5fdb72799e9d3541f93c"}