  We classify and explicitly describe homomorphisms of Verma modules for
conformal Galilei algebras $\mathfrak{cga}_\ell(d,{\mathbb C})$ with $d=1$ for
any integer value $\ell \in \mathbb{N}$. The homomorphisms are uniquely
determined by singular vectors as solutions of certain differential operators
of flag type, and identified with specific polynomials arising as coefficients
in the expansion of a parametric family of symmetric polynomials into power sum
symmetric polynomials.
