{"paper":{"title":"Hitchin's conjecture for simply-laced Lie algebras implies that for any simple Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Nathaniel Bushek, Shrawan Kumar","submitted_at":"2013-09-20T16:33:04Z","abstract_excerpt":"Let $\\g$ be any simple Lie algebra over $\\mathbb{C}$. Recall that there exists an embedding of $\\mathfrak{sl}_2$ into $\\g$, called a principal TDS, passing through a principal nilpotent element of $\\g$ and uniquely determined up to conjugation. Moreover, $\\wedge (\\g^*)^\\g$ is freely generated (in the super-graded sense) by primitive elements $\\omega_1, \\dots, \\omega_\\ell$, where $\\ell$ is the rank of $\\g$. N. Hitchin conjectured that for any primitive element $\\omega \\in \\wedge^d (\\g^*)^\\g$, there exists an irreducible $\\mathfrak{sl}_2$-submodule $V_\\omega \\subset \\g$ of dimension $d$ such tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5313","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"}