Tohoku Mathematical Journal

A characterization of symmetric Siegel domains by convexity of Cayley transform images

Chifune Kai

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Abstract

We show that a homogeneous Siegel domain is symmetric if and only if its Cayley transform image is convex. Moreover, this convexity forces the parameter of the Cayley transform to be specific, so that the Cayley transform coincides with the inverse of the Cayley transform introduced by Korányi and Wolf.

Article information

Source
Tohoku Math. J. (2), Volume 59, Number 1 (2007), 101-118.

Dates
First available in Project Euclid: 16 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1176734750

Digital Object Identifier
doi:10.2748/tmj/1176734750

Mathematical Reviews number (MathSciNet)
MR2321995

Zentralblatt MATH identifier
1201.32011

Subjects
Primary: 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]
Secondary: 43A85: Analysis on homogeneous spaces 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions

Keywords
Homogeneous Siegel domain symmetric Siegel domain Cayley transform normal $j$-algebra

Citation

Kai, Chifune. A characterization of symmetric Siegel domains by convexity of Cayley transform images. Tohoku Math. J. (2) 59 (2007), no. 1, 101--118. doi:10.2748/tmj/1176734750. https://projecteuclid.org/euclid.tmj/1176734750


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