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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 "},"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":"0809.4650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-09-26T14:57:19Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"6ea9f96da5c8d253f839ef430299e4bb487b3912a76271afd1e968f389bf459f","abstract_canon_sha256":"bdbc5317340abc69b2ae8f74ba8798723215246c7767c13aae5d20a2723727d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:33.446897Z","signature_b64":"7JRHfyoDnPJCUtd0HsWByUq4u9EIFdO3k4SWbUb/QTlaSgJsyTkMHvsv8UgTU5m2UpD99WhFuHXaIjWVMyESCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5668e5b8fa0a9adc9cf30a2e5b2cee5959ab5164155359931c7b7e2b73a6733","last_reissued_at":"2026-05-18T02:15:33.446234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:33.446234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Completeness of determinantal Hamiltonian flows on the matrix affine Poisson space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.SG","authors_text":"Michael Gekhtman, Milen Yakimov","submitted_at":"2008-09-26T14:57:19Z","abstract_excerpt":"The matrix affine Poisson space (M_{m,n}, pi_{m,n}) is the space of complex rectangular matrices equipped with a canonical quadratic Poisson structure which in the square case m=n reduces to the standard Poisson structure on GL_n(C). 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