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We consider the population of critical points generated from the criticalpoint of the master function with no variables, which is associated with thetrivial representation of the twisted affine Lie algebra $A^{(2)}_{2n}$. Thepopulation is naturally partitioned into an infinite collection of complexcells $\mathbb{C}^m$, where $m$ are some positive integers. For each cell wedefine an injective rational map $\mathbb{C}^m \to M(A^{(2)}_{2n})$ of the cellto the space $M(A^{(2)}_{2n})$ of Miura opers of type $A^{(2)}_{2n}$. We showthat the image of the map is invariant with respect to all mKdV flows on$M(A^{(2)}_{2n})$ and the image is point-wise fixed by all mKdV flows$\frac\partial{\partial t_r}$ with index $r$ greater than $4m$.

Critical points of master functions and mKdV hierarchy of type $A^{(2)}_{2n}$