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arXiv · 2111.06873

Elliptic hypergeometric function and $6j$-symbols for the SL(2,$\mathbb{C}$) group

S. E. Derkachov·G. A. Sarkissian·V. P. Spiridonov
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Abstract

We show that the complex hypergeometric function describing $6j$-symbols for $SL(2,\mathbb{C})$ group is a special degeneration of the $V$-function -- an elliptic analogue of the Euler-Gauss $_2F_1$ hypergeometric function. For this function, we derive mixed difference-recurrence relations as limiting forms of the elliptic hypergeometric equation and some symmetry transformations. At the intermediate steps of computations, there emerge a function describing the $6j$-symbols for the Faddeev modular double and the corresponding difference equations and symmetry transformations.

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BibTeXRIS

S. E. Derkachov, G. A. Sarkissian, V. P. Spiridonov. 2021-11-12. Elliptic hypergeometric function and $6j$-symbols for the SL(2,$\mathbb{C}$) group. https://doi.org/10.1134/s0040577922100087

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