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Theoretical and Mathematical Physics

, Volume 167, Issue 2, pp 567–576 | Cite as

Special Lagrangian fibrations on the flag variety F 3

  • N. A. TyurinEmail author
Article

Abstract

We propose a construction of a Lagrangian torus fibration of the full flag variety in 3 . In contrast to the classical fibration obtained from the Gelfand-Zeitlin system, the proposed fibration is special Lagrangian.

Keywords

flag variety Lagrangian torus pseudotoric structure special Lagrangian fibration 

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References

  1. 1.
    M. Audin, Torus Actions on Symplectic Manifolds (Progr. Math., Vol. 93), Birkhäuser, Basel (2004).zbMATHCrossRefGoogle Scholar
  2. 2.
    S. A. Belev and N. A. Tyurin, Math. Notes, 87, 43–51 (2010).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    N. A. Tyurin, Theor. Math. Phys., 162, 255–275 (2010).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    V. Guillemin and S. Sternberg, J. Funct. Anal., 52, 106–128 (1983).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    D. Auroux, J. Gökova Geom. Topol., 1, 51–91 (2007); arXiv:0706.3207v2 [math.SG] (2007).MathSciNetzbMATHGoogle Scholar
  6. 6.
    T. Nishinou, Y. Nohara, and K. Ueda, Adv. Math., 224, 648–706 (2010); arXiv:0810.3470v2 [math.SG] (2008).MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    N. A. Tyurin, “Twist tori and pseudotoric structures,” arXiv:1004.2574v1 [math.SG] (2010).Google Scholar

Copyright information

© MAIK/Nauka 2011

Authors and Affiliations

  1. 1.Joint Institute for Nuclear ResearchDubna, Moscow OblastRussia
  2. 2.Higher School of EconomicsMoscowRussia
  3. 3.Moscow State University of Railway Engineering (MIIT)MoscowRussia

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