Quiver varieties and Demazure modules

Details Quiver varieties and Demazure modules Quiver varieties and Demazure modules

2004-09-21

arxiv.org/abs/math/0409411v3

Math. Ann. 335 (2006), no. 1, 31-46

Mathematics

Representation Theory

14 pages, 2 figures; v2: Minor corrections and reference added; v3: Proofs of Proposition 6.1 and Theorem 8.1 corrected. This

Scientific paper

10.1007/s00208-005-0694-7

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 affine sl_2, 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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