Abstract
In this paper, the additional symmetries and the string equation of the [Formula: see text]-NKdV hierarchy are established basing on the Orlov–Shulman’s [Formula: see text] operator, and then some properties are also given. Next, we construct the quantum torus symmetry of the [Formula: see text]-NKdV hierarchy and further derive the quantum torus constraints on the tau function of the [Formula: see text]-NKdV hierarchy. Comparing to the [Formula: see text] infinite-dimensional Lie symmetry, this quantum torus symmetry has a nice algebraic structure with double indices. Finally, we study the ghost symmetry of the multicomponent [Formula: see text]-NKdV hierarchy.
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