Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions. (English) Zbl 0974.17016
Arnold, V. I. (ed.) et al., The Arnold-Gelfand mathematical seminars: geometry and singularity theory. Boston, MA: Birkhäuser. 171-204 (1997).
Several new results concerning \(6j\)-symbols are established and proved. It is shown that the elliptic \(6j\)-symbols have tetrahedral symmetry analogous to the well-known symmetry of the classical and quantum \(6j\)-symbols. Using a graphical calculus a relation between the elliptic \(6j\)-symbols and the trigonometric \(6j\)-symbols is established. The transformation properties of the elliptic \(6j\)-symbols under the natural action of the modular group \( SL_{2}\left( {\mathbb Z}\right) \) in the space of parameters are given.
For the entire collection see [Zbl 0857.00029].
For the entire collection see [Zbl 0857.00029].
Reviewer: Steven Duplij (Kharkov)
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 33D15 | Basic hypergeometric functions in one variable, \({}_r\phi_s\) |
| 82B23 | Exactly solvable models; Bethe ansatz |
| 33D80 | Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
