Poincaré series, exponents of affine Lie algebras, and McKay-Slodowy correspondence

Let N be a normal subgroup of a finite group G and V a fixed finite-dimensional G-module. The Poincaré series for the multiplicities of induced modules and restriction modules in the tensor algebra T(V)=⊕k≥0V⊗k are studied in connection with the McKay-Slodowy correspondence. In particular, it is shown that the closed formulas for the Poincaré series associated with the distinguished pairs of subgroups of SU2 give rise to the exponents of all untwisted and twisted affine Lie algebras except A2n(1).