A remark on the integrals of motion associated with level $k$ realization of the elliptic algebra $U_{q,p}(sl_2^)$

TL;DR

This paper introduces a one-parameter deformation of the level k free field realization of the elliptic algebra U_{q,p}(sl_2^), constructing infinitely many nonlocal integrals of motion expressed as integrals involving screening currents and elliptic theta functions.

Contribution

It provides a level k generalization of nonlocal integrals of motion for the elliptic algebra U_{q,p}(sl_2^), expanding the mathematical framework of integrable models.

Findings

Constructed a one-parameter deformation of the level k free field realization.

Derived infinitely many nonlocal integrals of motion involving elliptic theta functions.

Generalized previous results to arbitrary level k.

Abstract

We give one parameter deformation of level $k$ free field realization of the screening current of the elliptic algebra $U_{q,p}(sl_2^)$. By means of these free field realizations, we construct infinitly many commutative operators, which we call the nonlocal integrals of motion associated with level $k$ realization of the elliptic algebra $U_{q,p}(sl_2^)$. They are given as integrals involving a product of the screening current and elliptic theta functions. This paper give level $k$ generalization of the nonlocal integrals of motion given in [arXiv:0705.0427].