{"paper":{"title":"Two commuting operators associated with a tridiagonal pair","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Sarah Bockting-Conrad","submitted_at":"2011-10-15T19:25:51Z","abstract_excerpt":"Let \\K denote a field and let V denote a vector space over \\K with finite positive dimension. We consider an ordered pair of linear transformations A:V\\to V and A*:V \\to V that satisfy the following four conditions: (i) Each of A,A* is diagonalizable; (ii) there exists an ordering {V_i}_{i=0}^d of the eigenspaces of A such that A*V_i\\subseteq V_{i-1}+V_i+V_{i+1} for 0\\leq i\\leq d, where V_{-1}=0 and V_{d+1}=0; (iii) there exists an ordering {V*_i}_{i=0}^{\\delta} of the eigenspaces of A* such that AV*_i\\subseteq V*_{i-1}+V*_i+V*_{i+1} for 0\\leq i\\leq\\delta, where V*_{-1}=0 and V*_{\\delta+1}=0; "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3434","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"}