{"paper":{"title":"The Bruhat--Chevalley order on involutions of the hyperoctahedral group and combinatorics of $B$-orbit closures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mikhail V. Ignatyev","submitted_at":"2011-12-12T17:07:22Z","abstract_excerpt":"Let $G$ be the symplectic group, $\\Phi=C_n$ its root system, $B\\subset G$ its standard Borel subgroup, $W$ the Weyl group of $\\Phi$. To each involution $\\sigma\\in W$ one can assign the $B$-orbit $\\Omega_{\\sigma}$ contained in the dual space of the Lie algebra of the unipotent radical of $B$. We prove that $\\Omega_{\\sigma}$ is contained in the Zariski closure of $\\Omega_{\\tau}$ if and only of $\\sigma\\leq\\tau$ with respect to the Bruhat--Chevalley order. We also prove that $\\dim\\Omega_{\\sigma}$ is equal to $l(\\sigma)$, the length of $\\sigma$ in $W$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2624","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"}