Central European Journal of Mathematics
, Volume 3, Issue 2, pp 155182
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.
Keywords
Bethe Ansatz Miura opers flag varietiesMSC (2000)
82B23 17B67 14M15 Title
 Miura opers and critical points of master functions
 Journal

Central European Journal of Mathematics
Volume 3, Issue 2 , pp 155182
 Cover Date
 200506
 DOI
 10.2478/BF02479193
 Print ISSN
 18951074
 Online ISSN
 16443616
 Publisher
 Central European Science Journals
 Additional Links
 Topics
 Keywords

 Bethe Ansatz
 Miura opers
 flag varieties
 82B23
 17B67
 14M15
 Authors

 Evgeny Mukhin ^{(1)}
 Alexander Varchenko ^{(2)}
 Author Affiliations

 1. Department of Mathematical Sciences, Indiana University Purdue University Indianapolis, 402 North Blackford St., 462023216, Indianapolis, IN, USA
 2. Department of Mathematics, University of North Carolina at Chapel Hill, 275993250, Chapel Hill, NC, USA