Constructing vector-valued Siegel modular forms from scalar-valued Siegel modular forms

摘要

This paper gives a simple method for constructing vector-valued Siegel modular forms from scalar-valued ones. The method is efficient in producing the siblings of Delta, the smallest weight cusp forms that appear in low degrees. It also shows the strong relations between these modular forms of different degrees. We illustrate this by a number of examples.