  Recent asteroseismic observations by the $\it Kepler$ space mission have
revealed the dip fine structure in the period-spacing versus period diagram of
rapidly rotating $\gamma$ Doradus stars. Following the successful reproduction
of the dip structure by numerical calculations in previous studies, we present
in this paper the physical mechanism of how the dip is formed as a result of
the interaction between the gravito-inertial waves in the radiative envelope
and the pure inertial waves in the convective core. We analytically describe
the wave solutions in both of the radiative envelope and the convective core,
and match them at the interface to construct an eigenmode. We have found from
the analysis the following points: the dip structure is mainly controlled by a
parameter that has an inverse correlation with Brunt-V\"ais\"al\"a frequency at
the interface; the depth and the width of the dip is shallower and larger,
respectively, as the parameter gets large; the shape of the dip can be
approximated by the Lorentzian function; the period at the central position of
the dip is equal to or slightly smaller than that of the involved pure inertial
mode in the convective core. We have also understood based on the evolutionary
models of main-sequence stars that the parameter is inversely correlated with
the chemical composition gradient at the convective-core boundary. The dip
structure thus would provide information about the poorly-understood physical
processes, such as diffusion, convective overshooting and rotational mixing,
around the boundary between the convective core and the radiative envelope.
