{"paper":{"title":"The dominance hierarchy in root systems of Coxeter groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Xiang Fu","submitted_at":"2011-08-15T06:31:55Z","abstract_excerpt":"If $x$ and $y$ are roots in the root system with respect to the standard (Tits) geometric realization of a Coxeter group $W$, we say that $x$ \\emph{dominates} $y$ if for all $w\\in W$, $wy$ is a negative root whenever $wx$ is a negative root. We call a positive root \\emph{elementary} if it does not dominate any positive root other than itself. The set of all elementary roots is denoted by $\\E$. It has been proved by B. Brink and R. B. Howlett (Math. Ann. \\textbf{296} (1993), 179--190) that $\\E$ is finite if (and only if) $W$ is a finite-rank Coxeter group. Amongst other things, this finiteness "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2940","kind":"arxiv","version":2},"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"}