On the complex geometry of invariant domains in complexified symmetric spaces

Karl-Hermann Neeb

Displaying similar documents to “On the complex geometry of invariant domains in complexified symmetric spaces”

On the complex and convex geometry of Ol'shanskii semigroups

Karl-Hermann Neeb (1998)

Annales de l'institut Fourier

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To a pair of a Lie group $G$ and an open elliptic convex cone $W$ in its Lie algebra one associates a complex semigroup $S = G Exp (i W)$ which permits an action of $G \times G$ by biholomorphic mappings. In the case where $W$ is a vector space $S$ is a complex reductive group. In this paper we show that such semigroups are always Stein manifolds, that a biinvariant domain $D \subseteq S$ is Stein is and only if it is of the form $G Exp (D_{h})$ , with $D h \subseteq i W$ convex, that each holomorphic function on $D$ extends to the smallest biinvariant Stein domain...

A differential geometric characterization of invariant domains of holomorphy

Gregor Fels (1995)

Annales de l'institut Fourier

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Let $G = K^{ℂ}$ be a complex reductive group. We give a description both of domains $Ω \subset G$ and plurisubharmonic functions, which are invariant by the compact group, $K$ , acting on $G$ by (right) translation. This is done in terms of curvature of the associated Riemannian symmetric space $M : = G / K$ . Such an invariant domain $Ω$ with a smooth boundary is Stein if and only if the corresponding domain $Ω_{M} \subset M$ is geodesically convex and the sectional curvature of its boundary $S : = \partial Ω_{M}$ fulfills the condition $K^{S} (E) \geq K^{M} (E) + k (E, n)$ . The term $k (E, n)$ is explicitly...

Spherical functions on ordered symmetric spaces

Jacques Faraut, Joachim Hilgert, Gestur Ólafsson (1994)

Annales de l'institut Fourier

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We define on an ordered semi simple symmetric space $ℳ = G / H$ a family of spherical functions by an integral formula similar to the Harish-Chandra integral formula for spherical functions on a Riemannian symmetric space of non compact type. Associated with these spherical functions we define a spherical Laplace transform. This transform carries the composition product of invariant causal kernels onto the ordinary product. We invert this transform when $G$ is a complex group, $H$ a real form of $G$ ,...

Convexity for invariant differential operators on semisimple symmetric spaces

E. P. Van den Ban, H. Schlichtkrull (1993)

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Invariant convex sets and functions in Lie algebras.

K.H. Neeb (1996)

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Geometry of biinvariant subsets of complex semisimple Lie groups

Gregor Fels, Laura Geatti (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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