{"paper":{"title":"An Explicit Determination of the Springer Morphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Sean Rogers","submitted_at":"2017-01-06T03:49:21Z","abstract_excerpt":"Let $G$ be a simply connected semisimple algebraic group over $\\mathbb{C}$ and let $\\rho :G\\rightarrow GL(V_\\lambda)$ be an irreducible representation of highest weight $\\lambda$. Suppose that $\\rho$ has finite kernel. Springer defined adjoint-invariant regular map with Zariski dense image from the group to its Lie algebra, $\\theta_\\lambda:G\\rightarrow\\mathfrak{g}$, which depends on $\\lambda$ [Kumar]. By a lemma in Kumar's recent paper, $\\theta_\\lambda$ takes the maximal torus to its Lie algebra $\\mathfrak{t}$. Thus, for a given simple group $G$ and an irreducible representation $V_\\lambda$, o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01538","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"}