Central European Journal of Mathematics

, Volume 3, Issue 2, pp 155–182 | Cite as

Miura opers and critical points of master functions

  • Evgeny Mukhin
  • Alexander Varchenko


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 


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Copyright information

© Central European Science Journals 2005

Authors and Affiliations

  • Evgeny Mukhin
    • 1
  • Alexander Varchenko
    • 2
  1. 1.Department of Mathematical SciencesIndiana University Purdue University IndianapolisIndianapolisUSA
  2. 2.Department of MathematicsUniversity of North Carolina at Chapel HillChapel HillUSA

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