Infinite-dimensional hyperkähler manifolds associated with Hermitian-symmetric affine coadjoint orbits

Alice Barbara Tumpach

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

Similarity:

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 $M_{μ} : = Φ^{- 1} (K \cdot μ) / K$ is compact for all $μ$ . Then, we can define the “formal geometric quantization” of $M$ as $𝒬_{K}^{- \infty} (M) : = \sum_{μ \in \hat{K}} 𝒬 (M_{μ}) V_{μ}^{K} .$ The aim of this article is to study the functorial properties of the assignment $(M, K) \to 𝒬_{K}^{- \infty} (M)$ .

On Solvable Generalized Calabi-Yau Manifolds

Paolo de Bartolomeis, Adriano Tomassini (2006)

Annales de l’institut Fourier

Similarity:

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

Similarity:

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...

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

Natalia I. Bezvitnaya (2008)

Archivum Mathematicum

Similarity:

Connected weakly irreducible not irreducible subgroups of $Sp (1, n + 1) \subset SO (4, 4 n + 4)$ 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

Similarity:

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...

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

Formal geometric quantization

On Solvable Generalized Calabi-Yau Manifolds

Equations of some wonderful compactifications

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

Spherical gradient manifolds

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