Quiver varieties and Weyl group actions

George Lusztig

Displaying similar documents to “Quiver varieties and Weyl group actions”

Fixed points for reductive group actions on acyclic varieties

Martin Fankhauser (1995)

Annales de l'institut Fourier

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Let $X$ be a smooth, affine complex variety, which, considered as a complex manifold, has the singular $ℤ$ -cohomology of a point. Suppose that $G$ is a complex algebraic group acting algebraically on $X$ . Our main results are the following: if $G$ is semi-simple, then the generic fiber of the quotient map $π : X \to X / / G$ contains a dense orbit. If $G$ is connected and reductive, then the action has fixed points if $\dim X / / G \leq 3$ .

Rational smoothness of varieties of representations for quivers of Dynkin type

Philippe Caldero, Ralf Schiffler (2004)

Annales de l’institut Fourier

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We study the Zariski closures of orbits of representations of quivers of type $A$ , $D$ ou $E$ . With the help of Lusztig’s canonical base, we characterize the rationally smooth orbit closures and prove in particular that orbit closures are smooth if and only if they are rationally smooth.