  Two aspects of noncolliding diffusion processes have been extensively
studied. One of them is the fact that they are realized as harmonic Doob
transforms of absorbing particle systems in the Weyl chambers. Another aspect
is integrability in the sense that any spatio-temporal correlation function can
be expressed by a determinant. The purpose of the present paper is to clarify
the connection between these two aspects. We introduce a notion of
determinantal martingale and prove that, if the system has
determinantal-martingale representation, then it is determinantal. In order to
demonstrate the direct connection between the two aspects, we study three
processes.
