  Neutrinos are known to undergo flavor conversion among their three flavors.
In the theoretical modeling of core-collapse supernova (CCSN), there has been a
great deal of attention to recent discoveries of a new type of neutrino flavor
conversions, namely collisional flavor instability (CFI), in which the
instability is induced by the flavor-dependent decoherence due to the disparity
of neutrino-matter interactions among flavors. In this paper, we study how the
appearance of on-shell muons and associated neutrino-matter interactions can
impact CFIs based on linear stability analysis of flavor conversions. Some
striking results emerge from the present study. First, we analytically show
that breaking beta- and pair equilibrium is a necessary condition to trigger
CFIs. This also indicates that CFIs with on-shell muons could appear in $e
\tau$ and $\mu \tau$ neutrino mixing sectors in very high-density region
($\gtrsim 10^{13} {\rm g/cm^{3}}$), exhibiting a possibility of large impacts
of CFIs on CCSN. Second, resonance-like CFIs, having a much higher growth rate
than normal CFIs, can be triggered by muons. The resonance point of CFIs is
different between $e \tau$ and $\mu \tau$ sectors; the former (latter) occurs
at $\mu_{e (\mu)} = \mu_{n} - \mu_{p}$, where $\mu_{i}$ denotes the chemical
potential of $i$ constitute ($n$ and $p$ represent neutrons and protons,
respectively). Our result suggests that the non-linear evolution of CFI with
on-shell muons would induce flavor conversions with the complex interplay among
all three different neutrino-mixing sectors.
