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arXiv · 2509.23588

Non-local integrals of motion for deformed $W$-algebras of types $g=A_l, D_l, E_{6,7,8}$

Michio Jimbo·Takeo Kojima
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Abstract

We present an infinite set of non-local integrals of motion for deformed $W$-algebras of types $A_l, D_l$, and $E_{6,7,8}$. They can be regarded as a two-parameter deformation of trace of the monodromy matrix of the $g$-KdV theory. Commutativity of the non-local integrals of motion is shown in the case of $A_l$ and $D_l$ by a direct calculation. In the case of $E_{6,7,8}$ it is a conjecture.

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Michio Jimbo, Takeo Kojima. 2026-04-10. Non-local integrals of motion for deformed $W$-algebras of types $g=A_l, D_l, E_{6,7,8}$. https://arxiv.org/abs/2509.23588

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