{"paper":{"title":"Some $q$-exponential formulas involving the double lowering operator $\\psi$ for 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":"2019-07-02T04:19:43Z","abstract_excerpt":"Let $\\mathbb{K}$ denote an algebraically closed field and let $V$ denote a vector space over $\\mathbb{K}$ with finite positive dimension. Let $A,A^*$ denote a tridiagonal pair on $V$. We assume that $A,A^*$ belongs to a family of tridiagonal pairs said to have $q$-Racah type. Let $\\{U_i\\}_{i=0}^d$ and $\\{U_i^\\Downarrow\\}_{i=0}^{d}$ denote the first and second split decompositions of $V$. In an earlier paper we introduced a double lowering operator $\\psi:V\\to V$ with the notable feature that both $\\psi U_i\\subseteq U_{i-1}$ and $\\psi U_i^\\Downarrow\\subseteq U_{i-1}^\\Downarrow$ for $0\\leq i\\leq "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01157","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.01157/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"}