Displaying similar documents to “Dimensions of some affine Deligne–Lusztig varieties”

On a conjecture of Kottwitz and Rapoport

Qëndrim R. Gashi (2010)

Annales scientifiques de l'École Normale Supérieure

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We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur’s Inequality for all (connected) split and quasi-split unramified reductive groups. Our results are related to the non-emptiness of certain affine Deligne-Lusztig varieties.

On orbits of the automorphism group on an affine toric variety

Ivan Arzhantsev, Ivan Bazhov (2013)

Open Mathematics

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Let X be an affine toric variety. The total coordinates on X provide a canonical presentation X ¯ → X of X as a quotient of a vector space X ¯ by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.

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.

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 × 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.

Algebras with finitely generated invariant subalgebras

Ivan V. Arzhantsev (2003)

Annales de l’institut Fourier

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We classify all finitely generated integral algebras with a rational action of a reductive group such that any invariant subalgebra is finitely generated. Some results on affine embeddings of homogeneous spaces are also given.