, Volume 327, Issue 4, pp 671-721
Date: 30 Oct 2003

Reflection functors for quiver varieties and Weyl group actions

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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.

Mathematics Subject Classification (2000): Primary 53C26; Secondary 14D21, 16G20, 20F55, 33D80
Supported by the Grant-in-aid for Scientific Research (No.11740011), the Ministry of Education, Japan.