Displaying similar documents to “Equivariant degenerations of spherical modules for groups of type A ”

On bounded generalized Harish-Chandra modules

Ivan Penkov, Vera Serganova (2012)

Annales de l’institut Fourier

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Let 𝔤 be a complex reductive Lie algebra and 𝔨 ⊂ 𝔤 be any reductive in 𝔤 subalgebra. We call a ( 𝔤 , 𝔨 ) -module M bounded if the 𝔨 -multiplicities of M are uniformly bounded. In this paper we initiate a general study of simple bounded ( 𝔤 , 𝔨 ) -modules. We prove a strong necessary condition for a subalgebra 𝔨 to be bounded (Corollary 4.6), to admit an infinite-dimensional simple bounded ( 𝔤 , 𝔨 ) -module, and then establish a sufficient condition for a subalgebra 𝔨 to be bounded (Theorem 5.1). As a result we are...

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.

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...

Introduction to actions of algebraic groups

Michel Brion (2010)

Les cours du CIRM

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These notes present some fundamental results and examples in the theory of algebraic group actions, with special attention to the topics of geometric invariant theory and of spherical varieties. Their goal is to provide a self-contained introduction to more advanced lectures.

Proof of the Knop conjecture

Ivan V. Losev (2009)

Annales de l’institut Fourier

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In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoid are equivariantly isomorphic. We also state and prove a uniqueness property for (not necessarily smooth) affine spherical varieties.