Is the Luna stratification intrinsic?

Jochen Kuttler; Zinovy Reichstein

Displaying similar documents to “Is the Luna stratification intrinsic?”

Linear maps preserving orbits

Gerald W. Schwarz (2012)

Annales de l’institut Fourier

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Let $H \subset GL (V)$ be a connected complex reductive group where $V$ is a finite-dimensional complex vector space. Let $v \in V$ and let $G = {g \in GL (V) ∣ g H v = H v}$ . Following Raïs we say that the orbit $H v$ is if the identity component of $G$ is $H$ . If $H$ is semisimple, we say that $H v$ is for $H$ if the identity component of $G$ is an extension of $H$ by a torus. We classify the $H$ -orbits which are not (semi)-characteristic in many cases.

Relative property (T) and linear groups

Talia Fernós (2006)

Annales de l’institut Fourier

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Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group $Γ$ admits a special linear representation with non-amenable $R$ -Zariski closure if and only if it acts on an Abelian...

Equations of some wonderful compactifications

Pascal Hivert (2011)

Annales de l’institut Fourier

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De Concini and Procesi have defined the wonderful compactification $\bar{X}$ of a symmetric space $X = G / G^{σ}$ where $G$ is a complex semisimple adjoint group and $G^{σ}$ the subgroup of fixed points of $G$ by an involution $σ$ . It is a closed subvariety of a Grassmannian of the Lie algebra $𝔤$ of $G$ . In this paper we prove that, when the rank of $X$ is equal to the rank of $G$ , the variety is defined by linear equations. The set of equations expresses the fact that the invariant alternate trilinear form $w$ on $𝔤$ vanishes...

Smooth components of Springer fibers

William Graham, R. Zierau (2011)

Annales de l’institut Fourier

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This article studies components of Springer fibers for $𝔤𝔩 (n)$ that are associated to closed orbits of $G L (p) \times G L (q)$ on the flag variety of $G L (n), n = p + q$ . These components occur in any Springer fiber. In contrast to the case of arbitrary components, these components are smooth varieties. Using results of Barchini and Zierau we show these components are iterated bundles and are stable under the action of a maximal torus of $G L (n)$ . We prove that if $ℒ$ is a line bundle on the flag variety associated to a dominant weight,...

Spherical gradient manifolds

Christian Miebach, Henrik Stötzel (2010)

Annales de l’institut Fourier

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We study the action of a real-reductive group $G = K exp (𝔭)$ on a real-analytic submanifold $X$ of a Kähler manifold. We suppose that the action of $G$ extends holomorphically to an action of the complexified group $G^{ℂ}$ on this Kähler manifold such that the action of a maximal compact subgroup is Hamiltonian. The moment map induces a gradient map $μ_{𝔭} : X \to 𝔭$ . We show that $μ_{𝔭}$ almost separates the $K$ –orbits if and only if a minimal parabolic subgroup of $G$ has an open orbit. This generalizes Brion’s characterization of...