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Using Dynkin's classification, we prove that the restriction of an irreducible finite-dimensional representation of \\(\\mathrm G\\) to \\(\\mathrm G_0\\) determines the representation up to an outer automorphism of \\(\\mathrm G\\) preserving \\(\\mathrm G_0\\).\n  We extend this method to the diagonal embedding $\\mathrm G_0\\hookrightarrow \\mathrm G\\times \\mathrm G$ for the specific pairs "},"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":"2607.03804","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-04T10:24:36Z","cross_cats_sorted":[],"title_canon_sha256":"7271016c9e7ec7718f7f773fcfe265115470c7a7e08b89eb6b26505b103ec1d8","abstract_canon_sha256":"9b14122dbac55a2f7a6ef446821d33292aa4b47fb38882840859771fca7c9cf8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:18:08.463304Z","signature_b64":"GV48YdoTjQ/heoVzM7BrJG5Gp/e2Gp4jeh2Zt3oGb+pkOTYsQVaidzKzGh5MTi+B3JlbxLpE1aK6qeBtQrRnBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67cd19a779c68d70fd994e9a6fe16664f7978205c9c2a49a9fdbb1ce474abb77","last_reissued_at":"2026-07-07T02:18:08.462564Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:18:08.462564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness of Branching through regular unipotent elements","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Santosha Pattanayak, Santosh Nadimpalli","submitted_at":"2026-07-04T10:24:36Z","abstract_excerpt":"Let \\(\\mathrm G\\) be a complex simple algebraic group and let \\(\\mathrm G_0\\subset \\mathrm G\\) be a closed connected subgroup containing a regular unipotent element of \\(\\mathrm G\\), with semisimple rank at least \\(2\\). 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