  In this paper, we obtained character formulas of irreducible unitary
representations of $U(n, n+1)$ by using Howe's correspondence and the
Cauchy--Harish-Chandra integral. The representations of $U(n, n+1)$ we are
dealing with are obtained from a double lifting of a representation of $U(1)$
via the dual pairs $(U(1), U(1, 1))$ and $(U(1, 1), U(n, n+1))$.
