## Proceedings of the International Conference on Geometry, Integrability and Quantization

### 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

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436793435

Digital Object Identifier
doi:10.7546/giq-10-2009-11-55

Mathematical Reviews number (MathSciNet)
MR2757825

Zentralblatt MATH identifier
1182.53046

#### Citation

Clerc, Jean-Louis. Geometry of the Shilov Boundary of a Bounded Symmetric Domain. Proceedings of the Tenth International Conference on Geometry, Integrability and Quantization, 11--55, Avangard Prima, Sofia, Bulgaria, 2009. doi:10.7546/giq-10-2009-11-55. https://projecteuclid.org/euclid.pgiq/1436793435