Displaying similar documents to “Spherical Stein manifolds and the Weyl involution”

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 → 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...

Equivariant degenerations of spherical modules for groups of type A

Stavros Argyrios Papadakis, Bart Van Steirteghem (2012)

Annales de l’institut Fourier

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V. Alexeev and M. Brion introduced, for a given a complex reductive group, a moduli scheme of affine spherical varieties with prescribed weight monoid. We provide new examples of this moduli scheme by proving that it is an affine space when the given group is of type A and the prescribed weight monoid is that of a spherical module.

Spherical conjugacy classes and the Bruhat decomposition

Giovanna Carnovale (2009)

Annales de l’institut Fourier

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Let G be a connected, reductive algebraic group over an algebraically closed field of zero or good and odd characteristic. We characterize spherical conjugacy classes in G as those intersecting only Bruhat cells in G corresponding to involutions in the Weyl group of  G .

Classification of strict wonderful varieties

Paolo Bravi, Stéphanie Cupit-Foutou (2010)

Annales de l’institut Fourier

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In the setting of strict wonderful varieties we prove Luna’s conjecture, saying that wonderful varieties are classified by combinatorial objects, the so-called spherical systems. In particular, we prove that primitive strict wonderful varieties are mostly obtained from symmetric spaces, spherical nilpotent orbits and model spaces. To make the paper as self-contained as possible, we also gather some known results on these families and more generally on wonderful varieties.

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...