{"paper":{"title":"Classification of linkage systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Rafael Stekolshchik","submitted_at":"2014-06-11T20:14:55Z","abstract_excerpt":"A linkage diagram is obtained from the Carter diagram $\\Gamma$ by adding an extra root $\\gamma$, so that the resulting subset of roots is linearly independent. With every linkage diagram we associate the linkage label vector $\\gamma^{\\nabla}$, similar to Dynkin labels. The linkage diagrams connected under the action of the group $W^{\\vee}_{S}$ constitute the the linkage system $\\mathscr{L}(\\Gamma)$. For any simply-laced Carter diagram, the system $\\mathscr{L}(\\Gamma)$ is constructed. To obtain linkage diagrams $\\theta^{\\nabla}$, we use an easily verifiable criterion: $\\mathscr{B}^{\\vee}_{\\Gamm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3049","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"}