Central European Journal of Mathematics

, Volume 3, Issue 2, pp 155-182

First online:

Miura opers and critical points of master functions

  • Evgeny MukhinAffiliated withDepartment of Mathematical Sciences, Indiana University Purdue University Indianapolis
  • , Alexander VarchenkoAffiliated withDepartment of Mathematics, University of North Carolina at Chapel Hill

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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.


Bethe Ansatz Miura opers flag varieties

MSC (2000)

82B23 17B67 14M15