An infinite family of non-local integrals of motion is constructed for deformed W-algebras of types A_l, D_l, E_{6,7,8} as a two-parameter deformation of the monodromy trace in g-KdV theory, with commutativity proven for A/D and conjectured for E.
The Integrals of Motion for the Deformed Virasoro Algebra
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abstract
We explicitly construct two classes of infinitly many commutative operators in terms of the deformed Virasoro algebra. We call one of them local integrals and the other nonlocal one, since they can be regarded as elliptic deformations of the local and nonlocal integrals of motion obtained by V.Bazhanov, S.Lukyanov and Al.Zamolodchikov.
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Non-local integrals of motion for deformed $W$-algebras of types $g=A_l, D_l, E_{6,7,8}$
An infinite family of non-local integrals of motion is constructed for deformed W-algebras of types A_l, D_l, E_{6,7,8} as a two-parameter deformation of the monodromy trace in g-KdV theory, with commutativity proven for A/D and conjectured for E.