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The shape of a tridiagonal pair 伊藤, 達郎 Ito, Tatsuro 58 90015909 90015909 Terwilliger, Paul 15224 Let denote an algebraically closed field with characteristic 0. Let V denote a vector space over with finite positive dimension and let A,A* denote a tridiagonal pair on V. We make an assumption about this pair. Let q denote a nonzero scalar in that is not a root of unity. We assume A and A* satisfy the q-Serre relations A3A*−[3]A2A*A+[3]AA*A2−A*A3=0, A*3A−[3]A*2AA*+[3]A*AA*2−AA*3=0, where [3]=(q3−q−3)/(q−q−1). Let (ρ0,ρ1,…,ρd) denote the shape vector for A,A*. We show the entries in this shape vector are bounded above by binomial coefficients as follows: We obtain this result by displaying a spanning set for V. Mathematical subject codes: Primary: 17B37; secondary: 05E35; 15A21; 33C45; 33D45 金沢大学理学部 journal article Elsevier 2004-04-01 AM application/pdf Journal of Pure and Applied Algebra 1-3 188 145 160 0022-4049 https://kanazawa-u.repo.nii.ac.jp/record/10203/files/SC-ITO-T-shape3.pdf https://doi.org/10.24517/00010190 http://hdl.handle.net/2297/1862 https://kanazawa-u.repo.nii.ac.jp/records/10203 eng http://www.elsevier.com/locate/issn/00224049 http://www.sciencedirect.com/science/journal/00224049 https://doi.org/10.1016/j.jpaa.2003.10.002