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.
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Supported in part by NSF grant DMS-0140460
Supported in part by NSF grant DMS-0244579
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Mukhin, E., Varchenko, A. Miura opers and critical points of master functions. centr.eur.j.math. 3, 155–182 (2005). https://doi.org/10.2478/BF02479193
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DOI: https://doi.org/10.2478/BF02479193