  We present a linear stability analysis of the fast-pairwise neutrino flavor
conversion based on a result of our latest axisymmetric core-collapse supernova
(CCSN) simulation with full Boltzmann neutrino transport. In the CCSN
simulation, coherent asymmetric neutrino emissions of electron-type neutrinos
($\nu_{\rm e}$) and their anti-particles ($\bar{\nu}_{\rm e}$), in which the
asymmetry of $\nu_{\rm e}$ and $\bar{\nu}_{\rm e}$ is anti-correlated with each
other, occur at almost the same time as the onset of aspherical shock
expansion. We find that the asymmetric neutrino emissions play a crucial role
on occurrences of fast flavor conversions. The linear analysis shows that
unstable modes appear in both pre- and post-shock flows; for the latter they
appear only in the hemisphere of higher $\bar{\nu}_{\rm e}$ emissions (the same
hemisphere with stronger shock expansion). We analyze in depth the
characteristics of electron-lepton-number (ELN) crossing by closely inspecting
the angular distributions of neutrinos in momentum space. The ELN crossing
happens in various ways, and the property depends on the radius: in the
vicinity of neutron star, $\bar{\nu}_{\rm e}$ ($\nu_{\rm e}$) dominates over
$\nu_{\rm e}$ ($\bar{\nu}_{\rm e}$) in the forward (backward) direction: at the
larger radius the ELN crossing occurs in the opposite way. We also find that
the non-radial ELN crossing occurs at the boundary between no ELN crossing and
the radial one, which is an effect of genuine multi-D transport. Our findings
indicate that the collective neutrino oscillation may occur more commonly in
CCSNe and suggest that the CCSN community needs to accommodate these
oscillations self-consistently in the modelling of CCSNe.
