Miura opers and critical points of master functions

• Autorzy: Evgeny Mukhin , Alexander Varchenko
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2005
• Tom: 3
• Numer: 2
• Strony: 155-182

Daty

wydano

2005-06-01

online

2005-06-01

Twórcy

autor

Evgeny Mukhin

• Indiana University Purdue University Indianapolis

autor

Alexander Varchenko

• University of North Carolina at Chapel Hill

Bibliografia

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• [11] E. Mukhin and A. Varchenko: “Critical Points of Master Functions and Flag Varieties”, math.QA/0209017, (2002), pp. 1–49.
• [12] E. Mukhin and A. Varchenko: “Populations of solutions of the XXX Bethe equations associated to Kac-Moody algebras”, math.QA/0212092, (2002), pp. 1–8.
• [13] E. Mukhin and A. Varchenko: “Solutions to the XXX type Bethe Ansatz equations and flag varieties”, math.QA/0211321, (2002), pp. 1–32.
• [14] E. Mukhin and A. Varchenko: “Discrete Miura Opers and Solutions of the Bethe Ansatz Equations”, math.QA/0401137, (2004), pp. 1–26.
• [15] E. Mukhin and A. Varchenko: “Miura Opers and Critical Points of Master Functions”, math.QA/0312406, (2003), pp. 1–27.
• [16] E. Mukhin and A. Varchenko: “Multiple orthogonal polynomials and a counterexample to Gaudin Bethe Ansatz Conjecture”, math.QA/0501144, (2005), pp. 1–40.
• [17] N. Reshetikhin and A. Varchenko: “Quasiclassical asymptotics of solutions to the KZ equations”, In: Geometry, topology & physics. Conf. Proc. Lecture Notes Geom. Topology, VI, Internat. Press, Cambridge, MA, 1995, pp. 293–322.
• [18] I. Scherbak and A. Varchenko: “Critical point of functions, sl 2 representations and Fuchsian differential equations with only univalued solutions”, math.QA/0112269, (2001) pp. 1–25.
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Identyfikatory

DOI

10.2478/BF02479193