Miura Opers and Critical Points of Master Functions

Details Miura Opers and Critical Points of Master Functions Miura Opers and Critical Points of Master Functions

2003-12-22

arxiv.org/abs/math/0312406v2

Mathematics

Quantum Algebra

Latex, 27 pages

Scientific paper

Critical points of a master function associated to a simple Lie algebra \g come in families called the populations [MV1]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra \g^t. 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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