{"paper":{"title":"On involutions in the Weyl group and $B$-orbit closures in the orthogonal case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Mikhail V. Ignatyev","submitted_at":"2018-10-04T09:20:47Z","abstract_excerpt":"We study coadjoint $B$-orbits on $\\mathfrak{n}^*$, where $B$ is a Borel subgroup of a complex orthogonal group $G$, and $\\mathfrak{n}$ is the Lie algebra of the unipotent radical of $B$. To each basis involution $w$ in the Weyl group $W$ of $G$ one can assign the associated $B$-orbit $\\Omega_w$. We prove that, given basis involutions $\\sigma$, $\\tau$ in $W$, if the orbit $\\Omega_{\\sigma}$ is contained in the closure of the orbit $\\Omega_{\\tau}$ then $\\sigma$ is less than or equal to $\\tau$ with respect to the Bruhat order on $W$. For a basis involution $w$, we also compute the dimension of $\\O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02703","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"}