Mathematische Annalen

, Volume 327, Issue 4, pp 671–721

Reflection functors for quiver varieties and Weyl group actions

Authors

    • Department of MathematicsKyoto University
Article

DOI: 10.1007/s00208-003-0467-0

Cite this article as:
Nakajima, H. Math. Ann. (2003) 327: 671. doi:10.1007/s00208-003-0467-0

Abstract

We introduce reflectionfunctors on quiver varieties. They are hyper-Kähler isometries between quiver varieties with different parameters, related by elements in the Weyl group. The definition is motivated by the origial reflection functor given by Bernstein-Gelfand-Ponomarev [1], but they behave much nicely. They are isomorphisms and satisfy the Weyl group relations. As an application, we define Weyl group representations of homology groups of quiver varieties. They are analogues of Slodowy’s construction of Springer representations of the Weyl group.

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© Springer-Verlag Berlin Heidelberg 2003