Critical points of a master function associated to a simple Lie algebra come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra . 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.
@article{bwmeta1.element.doi-10_2478_BF02479193,
author = {Evgeny Mukhin and Alexander Varchenko},
title = {Miura opers and critical points of master functions},
journal = {Open Mathematics},
volume = {3},
year = {2005},
pages = {155-182},
zbl = {1108.82011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02479193}
}
Evgeny Mukhin; Alexander Varchenko. Miura opers and critical points of master functions. Open Mathematics, Tome 3 (2005) pp. 155-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02479193/
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