We describe hypergeometric solutions of the quantum differential equation of the cotangent bundle of a $$\mathfrak{g}\mathfrak{l}_n$$ partial flag variety. These hypergeometric solutions manifest the Landau-Ginzburg mirror symmetry for the cotangent bundle of a partial flag variety.
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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.
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