Journal of Geometry and Symmetry in Physics

Geometry of the Shilov Boundary of a Bounded Symmetric Domain

Jean-Louis Clerc

Abstract

In the first part, the theory of bounded symmetric domains is presented along two main approaches: as special cases of Riemannian symmetric spaces of the noncompact type on one hand, as unit balls in positive Hermitian Jordan triple systems on the other hand. In the second part, an invariant for triples in the Shilov boundary of such a domain is constructed. It generalizes an invariant constructed by E. Cartan for the unit sphere in $\mathbb{C}^2$ and also the triple Maslov index on the Lagrangian manifold.

Article information

Source
J. Geom. Symmetry Phys., Volume 13 (2009), 25-74.

Dates
First available in Project Euclid: 24 May 2017

https://projecteuclid.org/euclid.jgsp/1495591264

Digital Object Identifier
doi:10.7546/jgsp-13-2009-25-74

Mathematical Reviews number (MathSciNet)
MR2504587

Zentralblatt MATH identifier
1175.32011

Citation

Clerc, Jean-Louis. Geometry of the Shilov Boundary of a Bounded Symmetric Domain. J. Geom. Symmetry Phys. 13 (2009), 25--74. doi:10.7546/jgsp-13-2009-25-74. https://projecteuclid.org/euclid.jgsp/1495591264