{"paper":{"title":"Isomorphic induced modules and Dynkin diagram automorphisms of semisimple Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"C\\'edric Lecouvey, J\\'er\\'emie Guilhot","submitted_at":"2013-12-02T14:27:34Z","abstract_excerpt":"Consider a simple Lie algebra $\\mathfrak{g}$ and $\\overline{\\mathfrak{g}}% \\subset \\mathfrak{g}$ a Levi subalgebra. Two irreducible $\\overline{% \\mathfrak{g}}$-modules yield isomorphic inductions to $\\mathfrak{g}$ when their highest weights coincide up to conjugation by an element of the Weyl group $W$ of $\\mathfrak{g}$ which is also a Dynkin diagram automorphism of $% \\overline{\\mathfrak{g}}$. In this paper we study the converse problem: given two irreducible $\\overline{\\mathfrak{g}}$-modules of highest weight $\\mu $ and $\\nu $ whose inductions to $\\mathfrak{g}$ are isomorphic, can we conclud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0470","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":""},"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"}