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

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

2008-10-16

arxiv.org/abs/0810.2881v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

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].

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