  We construct an integral transformation intertwining the Gelfand-Tsetlin and
the (modified) Gauss-Givental realizations of principle series representations
of gl(3). This provides a direct identification of the corresponding integral
representations for the gl(3)-Whittaker function. The construction essentially
uses integral identities due to Barnes and Gustafson thus providing a basis for
their representation theory interpretation. The result of this paper might be
useful for constructing the explicit analytic realization of the mirror
symmetry map in the case of the flag manifold GL(3)/B.
