Mathematische Annalen

, Volume 324, Issue 4, pp 675–688 | Cite as

Crystal bases and quiver varieties

  • Yoshihisa Saito
Original article


We give a crystal structure on the set of all irreducible components of Lagrangian subvarieties of quiver varieties. One can show that, as a crystal, it is isomorphic to the crystal base of an irreducible highest weight representation of a quantized universal enveloping algebra.

Mathematics Subject Classification (2000): 17B35, 14D30, 16G20. 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Yoshihisa Saito
    • 1
  1. 1.Department of Mathematics, Hiroshima University, Higashi-Hiroshima 739-8526, Japan (e-mail: JP

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