Pullback formula for vector-valued Hermitian modular forms on $\mathrm{U}_{n,n}$

TL;DR

This paper derives a pullback formula for vector-valued Hermitian modular forms on CM fields and establishes conditions under which differential operators preserve automorphic properties.

Contribution

It introduces a pullback formula for vector-valued Hermitian modular forms on CM fields and characterizes differential operators that maintain automorphic properties.

Findings

Derived the pullback formula for vector-valued Hermitian modular forms.

Provided conditions for differential operators to preserve automorphic properties.

Enhanced understanding of automorphic forms on Hermitian symmetric domains.

Abstract

We give the pullback formula for vector-valued Hermitian modular forms on CM field. We also give the equivalent condition for a differential operator on Hermitian modular forms to preserve the automorphic properties.