{"paper":{"title":"On involutions in Weyl groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Jing Zhang, Jun Hu","submitted_at":"2016-09-27T15:19:51Z","abstract_excerpt":"Let $(W,S)$ be a Coxeter system and $\\ast$ be an automorphism of $W$ with order $\\leq 2$ such that $s^{\\ast}\\in S$ for any $s\\in S$. Let $I_{\\ast}$ be the set of twisted involutions relative to $\\ast$ in $W$. In this paper we consider the case when $\\ast=\\text{id}$ and study the braid $I_\\ast$-transformations between the reduced $I_\\ast$-expressions of involutions. If $W$ is the Weyl group of type $B_n$ or $D_n$, we explicitly describe a finite set of basic braid $I_\\ast$-transformations for all $n$ simultaneously, and show that any two reduced $I_\\ast$-expressions for a given involution can b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08494","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"}