{"paper":{"title":"Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mikhail V. Ignatyev","submitted_at":"2009-04-18T16:46:47Z","abstract_excerpt":"Let $\\Phi$ be a classical root system and $k$ be a field of sufficiently large characteristic. Let $G$ be the classical group over $k$ with the root system $\\Phi$, $U$ be its maximal unipotent subgroup and $\\mathfrak{u}$ be the Lie algebra of $U$. Let $D$ be an orthogonal subset of $\\Phi$ and $\\Omega$ be a coadjoint orbit of $U$ associated with $D$. We construct a polarization of $\\mathfrak{u}$ at the canonical form on $\\Omega$. We also find the dimension of $\\Omega$ in terms of the Weyl group of $\\Phi$. As a corollary, we determine all possible dimensions of irreducible complex represenations"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2841","kind":"arxiv","version":3},"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"}