{"paper":{"title":"Root systems and diagram calculus. III. Semi-Coxeter orbits of linkage diagrams and the Carter theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Rafael Stekolshchik","submitted_at":"2011-05-14T09:02:23Z","abstract_excerpt":"A diagram obtained from the Carter diagram $\\Gamma$ by adding one root together with its bonds such that the resulting subset of roots is linearly independent is said to be the {\\it linkage diagram}. Given a linkage diagram, we associate the linkage labels vector, which is introduced like the vector of Dynkin labels. Similarly to the dual Weyl group, we introduce the group $W^{\\vee}_L$ associated with $\\Gamma$, and we call it the dual partial Weyl group. The linkage labels vectors connected under the action of $W^{\\vee}_L$ constitute the linkage system $\\mathscr{L}(\\Gamma)$, which is similar t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2875","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"}