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Higher Lame Equations and Critical Points of Master Functions

E. Mukhin·V. Tarasov·A. Varchenko
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Abstract

Under certain conditions, we give an estimate from above on the number of differential equations of order $r+1$ with prescribed regular singular points, prescribed exponents at singular points, and having a quasi-polynomial flag of solutions. The estimate is given in terms of a suitable weight subspace of the tensor power $U(\n_-)^{\otimes (n-1)}$, where $n$ is the number of singular points in $\C$ and $U(\n_-)$ is the enveloping algebra of the nilpotent subalgebra of $\glg_{r+1}$.

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E. Mukhin, V. Tarasov, A. Varchenko. 2006-05-02. Higher Lame Equations and Critical Points of Master Functions. https://arxiv.org/abs/math/0601703

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