{"paper":{"title":"Rook placements in $A_n$ and combinatorics of $B$-orbit closures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anton S. Vasyukhin, Mikhail V. Ignatyev","submitted_at":"2013-10-11T15:20:50Z","abstract_excerpt":"Let $G$ be a complex reductive group, $B$ be a Borel subgroup of G, $\\nt$ be the Lie algebra of the unipotent radical of $B$, and $\\nt^*$ be its dual space. Let $\\Phi$ be the root system of $G$, and $\\Phi^+$ be the set of positive roots with respect to $B$.\n  A subset of $\\Phi^+$ is called a rook placement if it consists of roots with pairwise non-positive inner products. To each rook placement $D$ one can associate the coadjoint orbit $\\Omega_D$ of $B$ in $\\nt^*$. By definition, $\\Omega_D$ is the orbit of $f_D$, where $f_D$ is the sum of root covectors corresponging to the roots from $D$. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3164","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"}