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Quiver varieties and Demazure modules

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An Erratum to this article was published on 14 March 2010

Abstract

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 , 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.

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Authors and Affiliations

  1. The Fields Institute for Research in Mathematical Sciences and The University of Toronto, Toronto, Ontario, Canada

    Alistair Savage

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  1. Alistair Savage
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Correspondence to Alistair Savage.

Additional information

This research was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada.

An erratum to this article is available at http://dx.doi.org/10.1007/s00208-009-0477-7.

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Savage, A. Quiver varieties and Demazure modules . Math. Ann. 335, 31–46 (2006). https://doi.org/10.1007/s00208-005-0694-7

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  • DOI: https://doi.org/10.1007/s00208-005-0694-7

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