A remark on quiver varieties andweyl groups

Abstract

In this paper we define an action of the Weyl group on the quiver varieties $M_{m,\grl}(d,v)$ with generic $(m,\grl)$. To do it we describe a set of generators of the projective ring of a quiver variety. We also prove connectness 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.

47 pages, Latex2e

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• Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products
• Canonical bases and quiver varieties
• Tilting theoretical approach to moduli spaces over preprojective algebras
• Tensor products of unipotent characters of general linear groups over finite fields
• Namikawa-Weyl groups of affinizations of smooth Nakajima quiver varieties
• Spaltenstein varieties of pure dimension
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• Geometric construction of generators of CoHA of doubled quiver