  We classify the $(\mathfrak{g},K)$-modules generated by nearly holomorphic
Hilbert-Siegel modular forms by the global method. As an application, we study
the image of projection operators on the space of nearly holomorphic
Hilbert-Siegel modular forms with respect to infinitesimal characters in terms
of $(\mathfrak{g},K)$-modules.

Number Theory;Representation Theory