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An elementary approach to 6j-symbols (classical, quantum, rational, trigonometric, and elliptic)

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Abstract

Elliptic 6j-symbols first appeared in connection with solvable models of statistical mechanics. They include many interesting limit cases, such as quantum 6j-symbols (or q-Racah polynomials) and Wilson’s biorthogonal 10 W 9 functions. We give an elementary construction of elliptic 6j-symbols, which immediately implies several of their main properties. As a consequence, we obtain a new algebraic interpretation of elliptic 6j-symbols in terms of Sklyanin algebra representations.

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  1. Department of Mathematics Chalmers, University of Technology and Göteborg University, SE-412 96, Göteborg, Sweden

    Hjalmar Rosengren

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  1. Hjalmar Rosengren
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Correspondence to Hjalmar Rosengren.

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Dedicated to Richard Askey.

2000 Mathematics Subject Classification Primary—33D45, 33D80, 82B23

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Rosengren, H. An elementary approach to 6j-symbols (classical, quantum, rational, trigonometric, and elliptic). Ramanujan J 13, 131–166 (2007). https://doi.org/10.1007/s11139-006-0245-1

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