{"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\\). 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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03804","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.03804/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}