On Faddeev's Equation

Abstract

Faddeev' equations are a set-theoretical and an operator forms of the star-triangle equation. Known solutions of the quantum star-triangle equation, related to the Faddeev equations, are based on various forms of the modular double of the Weyl algebra including its cyclic representation. We show in this paper that Fadeev's equation also leads to a solution of the quantum star-triangle equation even in the case of a simple Weyl algebra with $|q|<1$. This paper can be seen as an addendum to the recent paper "V. Bazhanov and S. Sergeev, A distant descendant of the six-vertex model, arXiv:2310.08427".