{"paper":{"title":"The split decomposition of a tridiagonal pair","license":"","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Kazumasa Nomura, Paul Terwilliger","submitted_at":"2006-12-16T00:28:15Z","abstract_excerpt":"Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A:V \\to V$ and $A^*:V \\to V$ that satisfy (i)--(iv) below:\n  (i) Each of $A$, $A^*$ is diagonalizable.\n  (ii) There exists an ordering $V_{0},V_{1},...,V_{d}$ 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 $V_{-1}=0$, $V_{d+1}=0$.\n  (iii) There exists an ordering $V^*_{0},V^*_{1},...,V^*_{\\delta}$ of the eigenspaces of $A^*$ such that $A V^*_i \\subseteq V^*_{i-1} + V^*_{i} + V^*_{i+1}$ for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612460","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0612460/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}