{"paper":{"title":"Computing the Lusztig--Vogan Bijection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David B Rush","submitted_at":"2017-11-01T00:16:25Z","abstract_excerpt":"Let $G$ be a connected complex reductive algebraic group with Lie algebra $\\mathfrak{g}$. The Lusztig--Vogan bijection relates two bases for the bounded derived category of $G$-equivariant coherent sheaves on the nilpotent cone $\\mathcal{N}$ of $\\mathfrak{g}$. One basis is indexed by $\\Lambda^+$, the set of dominant weights of $G$, and the other by $\\Omega$, the set of pairs $(\\mathcal{O}, \\mathcal{E})$ consisting of a nilpotent orbit $\\mathcal{O} \\subset \\mathcal{N}$ and an irreducible $G$-equivariant vector bundle $\\mathcal{E} \\rightarrow \\mathcal{O}$. The existence of the Lusztig--Vogan bij"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00148","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"}