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

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