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Miura Opers and Critical Points of Master Functions

Evgeny Mukhin·Alexander Varchenko
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Abstract

Critical points of a master function associated to a simple Lie algebra \g come in families called the populations [MV1]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra \g^t. The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms of critical points composing the population.

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Evgeny Mukhin, Alexander Varchenko. 2004-10-12. Miura Opers and Critical Points of Master Functions. https://arxiv.org/abs/math/0312406

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