PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2005 | 3 | 2 | 155-182
Tytuł artykułu

Miura opers and critical points of master functions

Treść / Zawartość
Warianty tytułu
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
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
2
Strony
155-182
Opis fizyczny
Daty
wydano
2005-06-01
online
2005-06-01
Twórcy
  • University of North Carolina at Chapel Hill
Bibliografia
  • [1] A. Beilinson and V. Drinfeld: Opers, preprint.
  • [2] I.N. Bernshtein, I.M. Gel'fand and S.I. Gel'fand: “Structure of representations generated by vectors of highest weight”, Funct. Anal. Appl., Vol. 5, (1971), pp. 1–8. http://dx.doi.org/10.1007/BF01075841
  • [3] A. Borel: Linear algebraic groups, New York, W.A. Benjamin, 1969.
  • [4] L. Borisov and E. Mukhin: “Self-self-dual spaces of polynomials”, math. QA/0308128, (2003), pp. 1–38.
  • [5] V. Drinfeld and V. Sokolov: “Lie algebras and KdV type equations”, J. Sov. Math., Vol. 30, (1985), pp. 1975–2036. http://dx.doi.org/10.1007/BF02105860
  • [6] B. Feigin, E. Frenkel and N. Reshetikhin: “Gaudin model, Bethe Ansatz and Critical Level”, Commun. Math. Phys., Vol. 166, (1994), pp. 29–62. http://dx.doi.org/10.1007/BF02099300
  • [7] E. Frenkel: “Affine Algebras, Langlands Duality and Bethe Ansatz”, math.QA/9506003, (1999), pp. 1–34.
  • [8] E. Frenkel: “Opers on the projective line, flag manifolds and Bethe anzatz”, math.QA/0308269, (2003), pp. 1–48.
  • [9] J. Humphreys: Linear algebraic groups, Springer-Verlag, 1975.
  • [10] V. Kac: Infinite-dimensional Lie algebras, Cambridge University Press, 1990.
  • [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.
  • [19] V. Schechtman and A. Varchenko: “Arrangements of hyperplanes and Lie algebra homology”, Invent. Math. Vol. 106 (1991), pp. 139–194. http://dx.doi.org/10.1007/BF01243909
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02479193
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.