, Volume 3, Issue 2, pp 155-182

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.

Supported in part by NSF grant DMS-0140460
Supported in part by NSF grant DMS-0244579