{"paper":{"title":"Raising and lowering maps for tridiagonal pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CO","authors_text":"Paul Terwilliger","submitted_at":"2025-07-25T16:07:34Z","abstract_excerpt":"Let $V$ denote a nonzero finite-dimensional vector space. A tridiagonal pair on $V$ is an ordered pair $A, A^*$ of maps in ${\\rm End}(V)$ such that (i) each of $A, A^*$ is diagonalizable; (ii) there exists an ordering $\\lbrace V_i \\rbrace_{i=0}^d$ of the eigenspaces of $A$ such that $A^* V_i \\subseteq V_{i-1} + V_i + V_{i+1}$ $(0 \\leq i \\leq d)$, where $V_{-1} =0$ and $V_{d+1}=0$; (iii) there exists an ordering $\\lbrace V^*_i \\rbrace_{i=0}^\\delta$ of the eigenspaces of $A^*$ such that $A V^*_i \\subseteq V^*_{i-1} + V^*_i + V^*_{i+1}$ $(0 \\leq i \\leq \\delta)$, where $V^*_{-1} =0$ and $V^*_{\\del"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19400","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/2507.19400/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"}