  The O'Connell process is a softened version (a geometric lifting with a
parameter $a>0$) of the noncolliding Brownian motion such that neighboring
particles can change the order of positions in one dimension within the
characteristic length $a$. This process is not determinantal. Under a special
entrance law, however, Borodin and Corwin gave a Fredholm determinant
expression for the expectation of an observable, which is a softening of an
indicator of a particle position. We rewrite their integral kernel to a form
similar to the correlation kernels of determinantal processes and show, if the
number of particles is $N$, the rank of the matrix of the Fredholm determinant
is $N$. Then we give a representation for the quantity by using an $N$-particle
system of complex Brownian motions (CBMs). The complex function, which gives
the determinantal expression to the weight of CBM paths, is not entire, but in
the combinatorial limit $a \to 0$ it becomes an entire function providing
conformal martingales and the CBM representation for the noncolliding Brownian
motion is recovered.
