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Abstract for MSRI Preprint 2000-012

A remark on quiver varieties and Weyl groups

Andrea Maffei

In this paper we define an action of the Weyl group on the quiver varieties $M_{m,{\lambda}}(d,v)$ with generic $(m,{\lambda})$. To do it we describe a set of generators of the projective ring of a quiver variety. We also prove connectedness for the smooth quiver variety $M(d,v)$ and normality for $M_0(d,v)$ in the case of a quiver of finite type and $d-v$ a regular weight.