Fixed points for reductive group actions on acyclic varieties

Martin Fankhauser

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.