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

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arxiv math/0312310 v1 pith:2AO3WAAE submitted 2003-12-16 math.CA math-phmath.MPmath.QA

Hjalmar Rosengren This is my paper · ORCID
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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. The quantum loop algebra of $sl_2$ and $q$-Racah type bivariate functions

    math.QA 2026-07 conditional novelty 6.0 of 10

    Bivariate q-Racah-type functions are realized as overlaps of six distinguished eigenbases in tensor-product evaluation representations of L U_q sl2, one family linked to tridiagonal pairs and another conjecturally to ...

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