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• W3127372101 endingPage "106632" @default.
• W3127372101 startingPage "106632" @default.
• W3127372101 abstract "Let F denote a field, and let V denote a vector space over F with finite positive dimension. We consider an ordered pair of F-linear maps A:V→V and A⁎:V→V such that (i) each of A,A⁎ is diagonalizable; (ii) there exists an ordering {Vi}i=0d of the eigenspaces of A such that A⁎Vi⊆Vi−1+Vi+Vi+1 for 0≤i≤d, where V−1=0 and Vd+1=0; (iii) there exists an ordering {Vi⁎}i=0δ of the eigenspaces of A⁎ such that AVi⁎⊆Vi−1⁎+Vi⁎+Vi+1⁎ for 0≤i≤δ, where V−1⁎=0 and Vδ+1⁎=0; (iv) there does not exist a subspace U of V such that AU⊆U, A⁎U⊆U, U≠0, U≠V. We call such a pair a tridiagonal pair on V. We assume that A,A⁎ belongs to a family of tridiagonal pairs said to have q-Racah type. There is an infinite-dimensional algebra ⊠q called the q-tetrahedron algebra; it is generated by four copies of Uq(sl2) that are related in a certain way. Using A,A⁎ we construct two ⊠q-module structures on V. In this construction the two main ingredients are the double lowering map ψ:V→V due to Sarah Bockting-Conrad, and a certain invertible map W:V→V motivated by the spin model concept due to V. F. R. Jones." @default.
• W3127372101 created "2021-02-15" @default.
• W3127372101 creator A5059249005 @default.
• W3127372101 date "2021-08-01" @default.
• W3127372101 modified "2023-09-25" @default.
• W3127372101 title "Tridiagonal pairs of q-Racah type and the q-tetrahedron algebra" @default.
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• W3127372101 doi "https://doi.org/10.1016/j.jpaa.2020.106632" @default.
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