Cyclic Quantum Dilogarithm and Shift Operator

TL;DR

This paper constructs a shift operator from the cyclic quantum dilogarithm at roots of unity, providing a representation for Faddeev's current algebra, and demonstrates theta-function factorization via the Baxter-Bazhanov model's star-square equation.

Contribution

It introduces a new construction of the shift operator using cyclic quantum dilogarithm at roots of unity and extends the representation of Faddeev's current algebra.

Findings

Shift operator constructed from cyclic quantum dilogarithm at roots of unity.

Representation provided for Faddeev's current algebra.

Theta-function shown to be factorizable via the star-square equation.

Abstract

{}From the cyclic quantum dilogarithm the shift operator is constructed with $q$ is a root of unit and the representation is given for the current algebra introduced by Faddeev $et ~al$. It is shown that the theta-function is factorizable also in this case by using the star-square equation of the Baxter-Bazhanov model.