On the classification of $$({\mathfrak {g}},K)$$-modules generated by nearly holomorphic Hilbert–Siegel modular forms and projection operators

Abstract

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.