Hua operator on vector bundle: Application to AdS/CFT correspondence of Dirac fields

Hua’s theory of harmonic functions on classical domains is generalized to the theory on holomorphic vector bundles over classical domains and further on vector bundles over the real classical domains and quaternion classical domains. In case of the simplest quaternion classical domain there is a relation between Hua operator and Dirac operator, by which an AdS/CFT correspondence of Dirac fields is established.