Critical points of master functions and mKdV hierarchy of type A⁽²⁾_2n

2017/02/20 by Alexander Varchenko, Varchenko, Alexander, Tyler Woodruff +1
Mathematics · #Algebraic Geometry (math.AG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1702.06169

openalex publication_date 2017/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 A⁽²⁾_2n. The population is naturally partitioned into an infinite collection of complex cells ℂ^m, where m are some positive integers. For each cell we define an injective rational map ℂ^m → M(A⁽²⁾_2n) of the cell to the space M(A⁽²⁾_2n) of Miura opers of type A⁽²⁾_2n. We show that 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∂∂ t_r with index r greater than 4m.

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