We consider the population of critical points, generated from the critical point of the master function with no variables, which is associated with the trivial representation of the twisted affine Lie algebra ${C_{n}^{(1)}}$. The population is naturally partitioned into an infinite collection of complex cells ${\mathbb{C}^{m}}$, where m are positive integers. For each cell we define an injective rational map ${\mathbb{C}^{m}}\to M({C_{n}^{(1)}})$ of the cell to the space $M({C_{n}^{(1)}})$ of Miura opers of type ${C_{n}^{(1)}}$. We show that the image of the map is invariant with respect to all mKdV flows on $M({C_{n}^{(1)}})$ and the image is point-wise fixed by all mKdV flows $\frac{\partial }{\partial {t_{r}}}$ with index r greater than $2m$.

中文翻译：

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$ C ^ {（1）} _ n $类型的关键点和mKdV层次结构

我们考虑临界点的数量，这些临界点是从主函数的临界点生成的，没有变量，这与扭曲仿射李代数$ {C_ {n} ^ {（（1）}} $的琐碎表示有关。种群自然地被划分为无穷多个复杂单元$ {\ mathbb {C} ^ {m}} $，其中m是正整数。对于每个单元格，我们定义到单元格的M（{C_ {n} ^ {{（1）}}）$到空间$ M（{C_}的内射有理映射$ {\ mathbb {C} ^ {m}} \类型为{{C_ {n} ^ {（1）}} $的Miura opers的{n} ^ {（（1）}}）$美元。我们表明，映射图像对于$ M（{C_ {n} ^ {（1）}}）$上的所有mKdV流都是不变的，并且图像由所有mKdV流$ \ frac { \ partial} {\ partial {t_ {r}}} $，索引r大于$ 2m $。