Displaying similar documents to “Spherical gradient manifolds”

Spherical Stein manifolds and the Weyl involution

Dmitri Akhiezer (2009)

Annales de l’institut Fourier

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We consider an action of a connected compact Lie group on a Stein manifold by holomorphic transformations. We prove that the manifold is spherical if and only if there exists an antiholomorphic involution preserving each orbit. Moreover, for a spherical Stein manifold, we construct an antiholomorphic involution, which is equivariant with respect to the Weyl involution of the acting group, and show that this involution stabilizes each orbit. The construction uses some properties of spherical...

Linear maps preserving orbits

Gerald W. Schwarz (2012)

Annales de l’institut Fourier

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Let H ⊂ GL ( V ) be a connected complex reductive group where V is a finite-dimensional complex vector space. Let v ∈ V and let G = { g ∈ 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.

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 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 ) × 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,...

Limit formulas for groups with one conjugacy class of Cartan subgroups

Mladen Božičević (2008)

Annales de l’institut Fourier

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Limit formulas for the computation of the canonical measure on a nilpotent coadjoint orbit in terms of the canonical measures on regular semisimple coadjoint orbits arise naturally in the study of invariant eigendistributions on a reductive Lie algebra. In the present paper we consider a particular type of the limit formula for canonical measures which was proposed by Rossmann. The main technical tool in our analysis are the results of Schmid and Vilonen on the equivariant sheaves on...