# Miura opers and critical points of master functions

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## Abstract

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.

### Keywords

*Bethe Ansatz*

*Miura opers*

*flag varieties*

### MSC (2000)

*82B23*

*17B67*

*14M15*

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