Abstract :

In this introductory talk, we outline the relationship between hermitian symmetric spaces, of non-compact and compact type, and Jordan algebraic structures, the so-called Jordan triple systems. The Jordan theoretic approach to symmetric spaces is somewhat more direct than the traditional Lie theoretic approach. In particular, the most important geometric features such as Bergman metric, canonical line bundles and boundary structure can be expressed using Jordan algebraic invariants. The theory is illustrated by examples (projective space, Grassmannians and spin factors)