Bounded symmetric domains and derived geometric structures

Wilhelm Kaup

Displaying similar documents to “Bounded symmetric domains and derived geometric structures”

A triple ratio on the Silov boundary of a bounded symmetric domain

Jean-Louis Clerc (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $D$ be a Hermitian symmetric space of tube type, $S$ its Silov boundary and $G$ the neutral component of the group of bi-holomorphic diffeomorphisms of $D$ . Our main interest is in studying the action of $G$ on $S^{3} = S \times S \times S$ . Sections 1 and 2 are part of a joint work with B. Ørsted (see [4]). In Section 1, as a pedagogical introduction, we study the case where $D$ is the unit disc and $S$ is the circle. This is a fairly elementary and explicit case, where one can easily get a flavour of the more general results....

Continuous Reinhardt domains from a Jordan viewpoint

L. L. Stachó (2008)

Studia Mathematica

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As a natural extension of bounded complete Reinhardt domains in $ℂ^{N}$ to spaces of continuous functions, continuous Reinhardt domains (CRD) are bounded open connected solid sets in commutative C*-algebras with respect to the natural ordering. We give a complete parametric description for the structure of holomorphic isomorphisms between CRDs and characterize the partial Jordan triple structures which can be associated with some CRDs. On the basis of these results, we test two conjectures...

The extended future tube conjecture for SO(1, $𝑛$ )

Peter Heinzner, Patrick Schützdeller (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $C$ be the open upper light cone in $ℝ^{1 + n}$ with respect to the Lorentz product. The connected linear Lorentz group ${SO}_{ℝ} {(1, n)}^{0}$ acts on $C$ and therefore diagonally on the $N$ -fold product $T^{N}$ where $T = ℝ^{1 + n} + i C \subset ℂ^{1 + n} .$ We prove that the extended future tube ${SO}_{ℂ} (1, n) \cdot T^{N}$ is a domain of holomorphy.

Global Parametrization of Scalar Holomorphic Coadjoint Orbits of a Quasi-Hermitian Lie Group

Benjamin Cahen (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Let $G$ be a quasi-Hermitian Lie group with Lie algebra $𝔤$ and $K$ be a compactly embedded subgroup of $G$ . Let $ξ_{0}$ be a regular element of $𝔤^{*}$ which is fixed by $K$ . We give an explicit $G$ -equivariant diffeomorphism from a complex domain onto the coadjoint orbit $𝒪 (ξ_{0})$ of $ξ_{0}$ . This generalizes a result of [B. Cahen, Berezin quantization and holomorphic representations, Rend. Sem. Mat. Univ. Padova, to appear] concerning the case where $𝒪 (ξ_{0})$ is associated with a unitary irreducible representation of $G$ which...

The space $N_{*}$ of holomorphic functions on bounded symmetric domains

Manfred Stoll (1976)

Annales Polonici Mathematici

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On a class of inner maps

Edoardo Vesentini (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $f$ be a continuous map of the closure $\bar{Δ}$ of the open unit disc $Δ$ of $C$ into a unital associative Banach algebra $A$ , whose restriction to $Δ$ is holomorphic, and which satisfies the condition whereby $0 \notin σ (f (z)) \subset \bar{Δ}$ for all $z \in Δ$ and $σ (f (z)) \subset \partial Δ$ whenever $z \in \partial Δ$ (where $σ (x)$ is the spectrum of any $x \in A$ ). One of the basic results of the present paper is that $f$ is , that is to say, $σ (f (z))$ is then a compact subset of $\partial Δ$ that does not depend on $z$ for all $z \in \bar{Δ}$ . This fact will be applied to holomorphic self-maps of the open unit ball of some...

On local CR-transformations of Levi-degenerate group orbits in compact Hermitian symmetric spaces

Wilhelm Kaup, Dmitri Zaitsev (2006)

Journal of the European Mathematical Society

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We present a large class of homogeneous 2-nondegenerate CR-manifolds $M$ , both of hypersurface type and of arbitrarily high CR-codimension, with the following property: Every CR-equivalence between domains $U$ , $V$ in $M$ extends to a global real-analytic CR-automorphism of $M$ . We show that this class contains $G$ -orbits in Hermitian symmetric spaces $Z$ of compact type, where $G$ is a real form of the complex Lie group $Aut {(Z)}^{0}$ and $G$ has an open orbit that is a bounded symmetric domain of tube type. ...

A Kleinecke-Shirokov type condition with Jordan automorphisms

Matej Brešar, Ajda Fošner, Maja Fošner (2001)

Studia Mathematica

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Let φ be a Jordan automorphism of an algebra . The situation when an element a ∈ satisfies $1 / 2 (φ (a) + φ^{- 1} (a)) = a$ is considered. The result which we obtain implies the Kleinecke-Shirokov theorem and Jacobson’s lemma.