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When this connection is irreducible, we show that it is invariant by the standart involution and can be pushed down as a logarithmic $\\mathrm{sl}(2,\\mathbb C)$-connection over $\\mathbb P^1$ with poles at $0$, $1$, $t$ and $\\infty$. Therefore, the isomonodromic deformation $(E_t,\\nabla_t)$ of an irreducible Lam\\'e connection, when the elliptic curve $X_t$ varry in the Legendre family, is parametrized by a solution "},"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":"1410.4976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-18T16:22:00Z","cross_cats_sorted":[],"title_canon_sha256":"d2cd222edd77ad9b7b638b2b5dd22dea590f1f638cefa412e3decf37ad93c1af","abstract_canon_sha256":"73c2485b8b117377f89ae481b9cb80ce2e82269c93e45b4d9cd5b81e50cb1cb1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:47.312397Z","signature_b64":"3qdQBuHjhYiBpZLFdStT9iyNArZgJKXwiI+TL7qVozeOriGc7cZUqbYGh+JhjkXUOpEhBhSYk/tqMsAOfI5wBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2073135da05c3ee134e5ea2c81cc2f3f6d91134cf27cea52004cd09c3a7f47c4","last_reissued_at":"2026-05-18T02:39:47.311952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:47.311952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isomonodromic deformation of Lam\\'e connections, Painlev\\'e VI equation and Okamoto symetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Frank Loray","submitted_at":"2014-10-18T16:22:00Z","abstract_excerpt":"A Lam\\'e connection is a logarithmic $\\mathrm{sl}(2,\\mathbb C)$-connection $(E,\\nabla)$ over an elliptic curve $X:\\{y^2=x(x-1)(x-t)\\}$, $t\\not=0,1$, having a single pole at infinity. 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