Congruences between Klingen-Eisenstein series and cusp forms on ${\mathrm{U}}_{n,n}$

In this paper, we study congruences of Hecke eigenvalues between Hermitian Klingen-Eisenstein series and cusp forms on the unitary group ${\mathrm{U}}_{n,n}$ defined over the rational number field $\mathbb{Q}$. We also prove the rationality of the space of Hermitian automorphic forms and the integrality of their Hecke eigenvalues.