Title: Coherent state representations of the holomorphic automorphism group of a quasi-symmetric Siegel domain of type III

Abstract: The aim of this paper is to study the classification of generic coherent state representations of a Lie group and its connection to the structure theory of K\"{a}hler algebras. The group we deal with is the holomorphic automorphism group of a quasi-symmetric Siegel domain of type III. A method using the generalized Iwasawa decomposition is provided.