The R-operator for Modular Double

TL;DR

This paper constructs an R-operator for the modular double that solves the Yang-Baxter equation, acting on infinite-dimensional representations and built from fundamental operators related to permutation symmetries.

Contribution

It introduces a new R-operator for the modular double, expanding the understanding of integrable models with infinite-dimensional representations.

Findings

R-operator solves the Yang-Baxter equation for the modular double

Constructed from three fundamental operators generating S_4

Intertwines product of two L-operators in the modular double

Abstract

We construct the R-operator -- solution of the Yang-Baxter equation acting in the tensor product of two infinite-dimensional representations of Faddeev's modular double. This R-operator intertwines the product of two L-operators associated with the modular double and it is built from three basic operators generating the permutation group of four parameters S_4.