  Inspired by the Gan-Gross-Prasad conjecture and the descent problem for
classical groups, in this paper we study the descents of unipotent
representations of unitary groups over finite fields. We give the first
descents of unipotent representations explicitly, which are unipotent as well.
Our results include both the Bessel case and Fourier-Jacobi case, which are
related via theta correspondence.
