Remark on the Integrals of Motion Associated with Level $k$ Realization of the Elliptic Algebra $\mathrm{U}_{q,p}(\widehat{\mathfrak{sl}_2})$

Abstract

We give one parameter deformation of level $k$ free field realization of the screening current of the elliptic algebra $\mathrm{U}_{q,p}(\widehat{\mathfrak{sl}_2})$. By means of these free field realizations, we construct infinitely many commutative operators, which are called the nonlocal integrals of motion associated with the elliptic algebra $\mathrm{U}_{q,p}(\widehat{\mathfrak{sl}_2})$ for level $k$. 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 [1].