  Let $N$ be a normal subgroup of a finite group $G$ and $V$ be a fixed
finite-dimensional $G$-module. The Poincar\'{e} series for the multiplicities
of induced modules and restriction modules in the tensor algebra
$T(V)=\oplus_{k \geq 0}V^{\otimes k}$ are studied in connection with the
McKay-Slodowy correspondence. In particular, it is shown that the closed
formulas for the Poincar\'e series associated with the distinguished pairs of
subgroups of $\mathrm{SU}_2$ give rise to the exponents of all untwisted and
twisted affine Lie algebras except ${\rm A}_{2n}^{(1)}$.
