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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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