In this paper, the additional symmetries and the string equation of the q-NKdV hierarchy are established basing on the Orlov–Shulman’s M operator, and then some properties are also given. Next, we construct the quantum torus symmetry of the q-NKdV hierarchy and further derive the quantum torus constraints on the tau function of the q-NKdV hierarchy. Comparing to the W∞ 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 q-NKdV hierarchy.

中文翻译：

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q-NKdV 层次结构的对称性

在本文中，附加对称性和弦方程q-NKdV 层次结构是基于 Orlov-Shulman 的米运算符，然后还给出了一些属性。接下来，我们构建了量子环面对称性q-NKdV 层次结构，并进一步推导出对 tau 函数的量子环面约束q-NKdV 层次结构。比较W∞无限维李对称性，这种量子环面对称性具有良好的双指数代数结构。最后，我们研究了多分量的鬼对称性q-NKdV 层次结构。