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2003 | 1 | 2 | 238-271
Tytuł artykułu

Solutions to the XXX type Bethe ansatz equations and flag varieties

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EN
Abstrakty
EN
We consider a version of the A N Bethe equation of XXX type and introduce a reporduction procedure constructing new solutions of this equation from a given one. The set of all solutions obtained from a given one is called a population. We show that a population is isomorphic to the sl N+1 flag variety and that the populations are in one-to-one correspondence with intersection points of suitable Schubert cycles in a Grassmanian variety. We also obtain similar results for the root systems B N and C N. Populations of B N and C N type are isomorphic to the flag varieties of C N and B N types respectively.
Wydawca
Czasopismo
Rocznik
Tom
1
Numer
2
Strony
238-271
Opis fizyczny
Daty
wydano
2003-06-01
online
2003-06-01
Twórcy
autor
autor
Bibliografia
  • [1] N.M. Bogoliubov, A.G. Izergin, V.E. Korepin: Quantum Inverse Scattering Method and Correlation Functions, Cambridge University Press, Cambridge, 1993.
  • [2] W. Fulton: Intersection Theory, Springer-Verlag, 1984.
  • [3] L.D. Faddeev: “Lectures on quantum inverse scattering method”, In: X-C. Song. ed.: Integrable Systems, Nankai Lectures on Math Phys. (1987), World Scientific, Singapore, 1990, pp. 23–70.
  • [4] L.D. Faddeev and L.A. Takhtajan: “Quantum inverse problem method and the Heisenberg XXZ model”, Russian Math. Survey, Vol. 34, (1979), pp. 11–68.
  • [5] Ph. Griffiths, J. Harris: Principles of algebraic geometry, A Whiley-Interscience Publication, 1994.
  • [6] E. Mukhin and A. Varchenko: “Critical Points of Master Functions and Flag Varieties”, math.QA/0209017, (2002), pp. 1–49.
  • [7] E. Mukhin and A. Varchenko: “The quantized Knizhnik-Zamolodchikov equation in tensor products of irreducible sl(2)-modules”, In: Calogero-Moser-Sutherland Models workshop, Springer, 2000, pp. 347–384.
  • [8] E. Mukhin and A. Varchenko: “Populations of solutions of the XXX Bethe equations associated to Kac-Moody algebras”, math.QA/0212092, (2002), pp. 1–7.
  • [9] V. Tarasov and A. Varchenko: “Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras”, Invent. math., Vol. 128, (1997), pp. 501–588. http://dx.doi.org/10.1007/s002220050151
  • [10] V. Tarasov and A. Varchenko: “Completeness of Bethe vectors and Difference equations with Regular Singular points”, International Mathematics Research Notices, Vol. 13, (1995), pp. 637–669. http://dx.doi.org/10.1155/S1073792895000377
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02476011
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