Of Hermitian Symmetric Space

The goal of this paper is to describe Hermitian symmetric spaces. There are three basic types of symmetric space: compact, noncompact, and Euclidean, defined in terms of properties of g, the Lie algebra of its group of isometries. Our main goal is to prove that those of noncompact type are exactly the bounded symmetric domains in C~n with Riemannian structure given by the Bergman metric, and to characterize the irreducible Hermitian symmetric spaces.Chapter 1 gives basic definitions and properties of Hermitian symmetric spaces, and discusses the symmetric spaces of non-compact type. We discuss bounded symmetric domains in C~n in Chapter 2 and give the main result. The characterization of irreducible Hermitian symmetric spaces are given in chapter 3.