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Miura opers and critical points of master functions

Evgeny Mukhin, Alexander Varchenko (2005)

Open Mathematics

Critical points of a master function associated to a simple Lie algebra 𝔤 come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra t 𝔤 . 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...

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