Fixed points for reductive group actions on acyclic varieties

Martin Fankhauser

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Displaying similar documents to “Fixed points for reductive group actions on acyclic varieties”

Reductive group actions on affine varieties and their doubling

Dmitri I. Panyushev (1995)

Annales de l'institut Fourier

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We study $G$ -actions of the form $(G : X \times X^{*})$ , where $X^{*}$ is the dual (to $X$ ) $G$ -variety. These actions are called the doubled ones. A geometric interpretation of the complexity of the action $(G : X)$ is given. It is shown that the doubled actions have a number of nice properties, if $X$ is spherical or of complexity one.

Quiver varieties and Weyl group actions

George Lusztig (2000)

Annales de l'institut Fourier

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The cohomology of Nakajima’s varieties is known to carry a natural Weyl group action. Here this fact is established using the method of intersection cohomology, in analogy with the definition of Springer’s representations.