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Miura opers and critical points of master functions

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Mukhin E., Varchenko A.

Open Mathematics

2005

tom 3

nr 2

155-182

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

Ograniczanie wyników

1 Open Mathematics

1 Mukhin E.

1 Varchenko A.

1 2005

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Miura opers and critical points of master functions