{"paper":{"title":"Combinatorics of $B$-orbits and Bruhat--Chevalley order on involutions","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":"2011-01-11T19:51:59Z","abstract_excerpt":"Let $B$ be the group of invertible upper-triangular complex $n\\times n$ matrices, $\\mathfrak{u}$ the space of upper-triangular complex matrices with zeroes on the diagonal and $\\mathfrak{u}^*$ its dual space. The group $B$ acts on $\\mathfrak{u}^*$ by $(g.f)(x)=f(gxg^{-1})$, $g\\in B$, $f\\in\\mathfrak{u}^*$, $x\\in\\mathfrak{u}$.\n  To each involution $\\sigma$ in $S_n$, the symmetric group on $n$ letters, one can assign the $B$-orbit $\\Omega_{\\sigma}\\in\\mathfrak{u}^*$. We present a combinatorial description of the partial order on the set of involutions induced by the orbit closures. The answer is g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2189","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"}