Vector-valued Siegel modular forms

Vector-valued Siegel modular forms are the natural generalization
of elliptic modular forms (holomorphic functions on the upper half-plane
invariant under a certain action of the group SL(2,Z)). By contrast with
the case of elliptic modular forms, easily accessible examples of
vector-valued Siegel modular forms have been very sparse.
In this talk, after summarizing the basic concepts of vector-valued Siegel
modular forms, we explain a method to build them by looking at the Taylor expansion of scalar-valued ones (joint work with Gerard van der Geer).