{"paper":{"title":"Lifting of elements of Weyl groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jeffrey Adams, Xuhua He","submitted_at":"2016-08-01T18:04:27Z","abstract_excerpt":"Suppose $G$ is a reductive algebraic group, $T$ is a Cartan subgroup, $N=\\text{Norm}(T)$, and $W=N/T$ is the Weyl group. If $w\\in W$ has order $d$, it is natural to ask about the orders lifts of $w$ to $N$. It is straightforward to see that the minimal order of a lift of $w$ has order $d$ or $2d$, but it can be a subtle question which holds. We first consider the question of when $W$ itself lifts to a subgroup of $N$ (in which case every element of $W$ lifts to an element of $N$ of the same order). We then consider two natural classes of elements: regular and elliptic. In the latter case all l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00510","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"}