A REMARK ON QUIVER VARIETIES AND WEYL GROUPS

ANDREA MAFFEI

Abstract. In this paper we define an action of the Weyl group on the quiver varieties M_{m,λ}(d, v) with generic (m, λ). 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.