  Given a regular supercuspidal representation $\rho$ of the Levi subgroup $M$
of a standard parabolic subgroup $P=MN$ in a connected reductive group $G$
defined over a non-archimedean local field $F$, we serve you a Rodier type
structure theorem which provides us a geometrical parametrization of the set
$JH(Ind^G_P(\rho))$ of Jordan--H{\"o}lder constituents of the Harish-Chandra
parabolic induction representation $Ind^G_P(\rho)$, vastly generalizing Rodier
structure theorem for $P=B=TU$ Borel subgroup of a connected split reductive
group about 40 years ago. Our novel contribution is to overcome the essential
difficulty that the relative Weyl group $W_M=N_G(M)/M$ is not a coxeter group
in general, as opposed to the well-known fact that the Weyl group
$W_T=N_G(T)/T$ is a coxeter group. Indeed, such a beautiful structure theorem
also holds for finite central covering groups.
