{"paper":{"title":"On $\\bbf_q$-rational structure of nilpotent orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Bin Shu, Brian Parshall, Semra Kaptanoglu","submitted_at":"2007-03-18T20:25:07Z","abstract_excerpt":"Let $G$ be a simple algebraic group and $\\ggg=\\Lie(G)$ over $k=\\bar\\bbf_q$ where $q$ is a power of the prime characteristic of $k$, and $F$ a Frobenius morphism on $G$ which can be defined naturally on $\\ggg$. In this paper, we investigate the relation between $F$-stable restricted modules of $\\ggg$ and closed conical subvarieties defined over $\\bbf_q$ in the null cone $\\cn(\\ggg)$ of $\\ggg$. Furthermore, we clearly investigate the $\\bbf_q$-rational structure for all nilpotent orbits in $\\ggg$ under the adjoint action of $G$ when the characteristic of $k$ is good for $G$ and bigger than 3. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703527","kind":"arxiv","version":4},"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"}