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

TL;DR

This paper classifies certain mathematical modules generated by nearly holomorphic Hilbert-Siegel modular forms using a global method, and analyzes the effect of projection operators on these modules based on their infinitesimal characters.

Contribution

It provides a new classification of $(rak{g},K)$-modules generated by nearly holomorphic Hilbert-Siegel modular forms and examines the impact of projection operators on these modules.

Findings

Classification of $(rak{g},K)$-modules generated by nearly holomorphic Hilbert-Siegel modular forms.

Description of the image of projection operators in terms of infinitesimal characters.

Application of the global method to module classification.

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.