Mathematische Annalen

, Volume 335, Issue 1, pp 31–46 | Cite as

Quiver varieties and Demazure modules

  • Alistair SavageEmail author


Using subvarieties, which we call Demazure quiver varieties, of the quiver varieties of Nakajima, we give a geometric realization of Demazure modules of Kac-Moody algebras with symmetric Cartan data. We give a natural geometric characterization of the extremal weights of a representation and show that Lusztig's semicanonical basis is compatible with the filtration of a representation by Demazure modules. For the case of Open image in new window , we give a characterization of the Demazure quiver variety in terms of a nilpotency condition on quiver representations and an explicit combinatorial description of the Demazure crystal in terms of Young pyramids.

Mathematics Subject Classification (2000)

Primary 16G20 17B37 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.The Fields Institute for Research in Mathematical Sciences and The University of TorontoTorontoCanada

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