  We derive a Givental-type stationary phase integral representation for the
specified $\Gr_{m,N}$-Whittaker function introduced in \cite{GLO2}, which
presumably describes the $S^1\times U_N$-equivariant Gromov-Witten invariants
of Grassmann variety $\Gr_{m,N}$. Our main tool is a generalization of
Whittaker model for principal series $\CU(\frak{gl}_N)$-modules. In particular,
our construction includes a representation theory interpretation of the
Batyrev--Ciocan-Fontanine--Kim--van Straten toric degeneration of Grassmannian,
providing a direct connection between this toric degeneration of $\Gr_{m,N}$
and total positivity for unipotent matrices.
