Displaying similar documents to “Infinite-dimensional hyperkähler manifolds associated with Hermitian-symmetric affine coadjoint orbits”

Formal geometric quantization

Paul-Émile Paradan (2009)

Annales de l’institut Fourier

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Let K be a compact Lie group acting in a Hamiltonian way on a symplectic manifold ( M , Ω ) which is pre-quantized by a Kostant-Souriau line bundle. We suppose here that the moment map Φ is proper so that the reduced space M μ : = Φ - 1 ( K · μ ) / K is compact for all μ . Then, we can define the “formal geometric quantization” of M as 𝒬 K - ∞ ( M ) : = ∑ μ ∈ K ^ 𝒬 ( M μ ) V μ K . The aim of this article is to study the functorial properties of the assignment ( M , K ) → 𝒬 K - ∞ ( M ) .

On Solvable Generalized Calabi-Yau Manifolds

Paolo de Bartolomeis, Adriano Tomassini (2006)

Annales de l’institut Fourier

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We give an example of a compact 6-dimensional non-Kähler symplectic manifold ( M , κ ) that satisfies the Hard Lefschetz Condition. Moreover, it is showed that ( M , κ ) is a special generalized Calabi-Yau manifold.

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...

Weakly irreducible subgroups of Sp ( 1 , n + 1 )

Natalia I. Bezvitnaya (2008)

Archivum Mathematicum

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Connected weakly irreducible not irreducible subgroups of Sp ( 1 , n + 1 ) ⊂ SO ( 4 , 4 n + 4 ) that satisfy a certain additional condition are classified. This will be used to classify connected holonomy groups of pseudo-hyper-Kählerian manifolds of index 4.

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...