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It was proved for the other orbits in [M5] when G_R is of non-Hermitian type. In this paper, we prove the conjecture for an arbitrary non-closed K_C-orbit when G_R is of Hermitian type. Thus the conjecture is completely solved affirmatively."},"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":"math/0410302","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2004-10-13T01:24:57Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e53e881db2d1c66823290bf73c98c4b47036e948860e29372ef48fb3c158aaa9","abstract_canon_sha256":"4b9d0b1742cc6e82fdfc3d52e3007fe2d955697517f9fdb59f28ae9530156a19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:31.203801Z","signature_b64":"ZLWmczBu3xYzeV9hqOl+YgNCD1hzvoiriXHMU5rakc+76d8+Lc6eaTdSpgq8iXU/J02g/E9lA7cP0wls51GiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6316819aa57fcc126535903036ff57c10adeb975aa66cb49103c999539056afa","last_reissued_at":"2026-05-18T01:19:31.203125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:31.203125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivalence of domains arising from duality of orbits on flag manifolds III","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Toshihiko Matsuki","submitted_at":"2004-10-13T01:24:57Z","abstract_excerpt":"In [GM1], we defined a G_R-K_C invariant subset C(S) of G_C for each K_C-orbit S on every flag manifold G_C/P and conjectured that the connected component C(S)_0 of the identity would be equal to the Akhiezer-Gindikin domain D if S is of nonholomorphic type. This conjecture was proved for closed S in [WZ2,WZ3,FH,M4] and for open S in [M4]. It was proved for the other orbits in [M5] when G_R is of non-Hermitian type. In this paper, we prove the conjecture for an arbitrary non-closed K_C-orbit when G_R is of Hermitian type. 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