Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions

1997 ◽  
pp. 171-204 ◽  
Author(s):  
Igor B. Frenkel ◽  
Vladimir G. Turaev
Keyword(s):  
Hypergeometric Functions ◽  
Baxter Equation ◽  
Elliptic Solutions

A FAMILY OF FACE MODELS RELATED TO ZN-SYMMETRIC VERTEX MODEL OF BELAVIN

2004 ◽  
Vol 19 (supp02) ◽  
pp. 478-509
Author(s):  
Y. YAMADA
Keyword(s):  
Baxter Equation ◽  
Vertex Model ◽  
Face Type ◽  
The Face ◽  
Elliptic Solutions ◽  
Intertwining Relation

We present face-type elliptic solutions to the Yang-Baxter equation. They have 2N-2 real parameters. When specializing them to definite values, we recover the various models so far known. The intertwining relation between the face models above and the ZN-symmetric vertex model of Belavin is also given.

GENERALIZED SKLYANIN ALGEBRA

1991 ◽  
Vol 06 (39) ◽  
pp. 3635-3640 ◽  
Author(s):  
YAS-HIRO QUANO ◽  
AKIRA FUJII
Keyword(s):  
Lie Algebra ◽  
Universal Enveloping Algebra ◽  
Baxter Equation ◽  
Enveloping Algebra ◽  
Elliptic Solutions ◽  
Sklyanin Algebra

We propose a [Formula: see text]-Sklyanin algebra to shed new light on elliptic solutions of the Yang–Baxter equation. This object gives a quadratic generalization of the universal enveloping algebra of the Lie algebra [Formula: see text]. We also clarify the meaning of the parameters contained in it.

scholarly journals New Elliptic Solutions of the Yang–Baxter Equation

2016 ◽  
Vol 345 (2) ◽  
pp. 507-543 ◽  
Author(s):  
D. Chicherin ◽  
S. E. Derkachov ◽  
V. P. Spiridonov
Keyword(s):  
Baxter Equation ◽  
Elliptic Solutions

scholarly journals Comments on the multi-spin solution to the Yang–Baxter equation and basic hypergeometric sum/integral identity

2019 ◽  
Vol 34 (18) ◽  
pp. 1950140 ◽  
Author(s):  
Ilmar Gahramanov ◽  
Shahriyar Jafarzade
Keyword(s):  
Statistical Mechanics ◽  
Integral Identity ◽  
Hypergeometric Functions ◽  
Three Dimensional ◽  
Spin Model ◽  
Baxter Equation ◽  
Lattice Spin ◽  
Integrable Lattice ◽  
Basic Hypergeometric Functions

We present a multi-spin solution to the Yang–Baxter equation (YBE). The solution corresponds to the integrable lattice spin model of statistical mechanics with positive Boltzmann weights and parametrized in terms of the basic hypergeometric functions. We obtain this solution from a nontrivial basic hypergeometric sum-integral identity which originates from the equality of supersymmetric indices for certain three-dimensional [Formula: see text] = 2 Seiberg dual theories.

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