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

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 ${}_2{F}_1$ 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.

19 pages

References in corpus (3)

• Properties of generalized univariate hypergeometric functions
• Exact solution of the Faddeev-Volkov model
• Complex hypergeometric functions and integrable many-body problems

Cited by in corpus (4)

• A parafermionic hypergeometric function and supersymmetric 6j-symbols
• Complex and rational hypergeometric functions on root systems
• Complex rational Ruijsenaars model. The two-particle case
• From hyperbolic to complex Euler integrals