Fourier Coefficients and Algebraic Cusp Forms on U(2,n)

We establish a theory of scalar Fourier coefficients for a class of non-holomorphic, automorphic forms on the quaternionic real Lie group U(2,n). By studying the theta lifts of holomorphic modular forms from U(1,1), we apply this theory to obtain examples of non-holomorphic cusp forms on U(2,n) whose Fourier coefficients are algebraic numbers.