  The Lusztig-Shoji algorithm is generalized to a complex reflection group $W$
and give us a version of the Springer correspondence of $W$. We show that the
combinatorics of generalized Springer correspondences of dihedral groups of
order $2n$ exhibit the Brauer-Humphreys type reciprocity as in the case of Weyl
groups for odd $n$, and these constitute a major portion of the stratification
of the natural module categories attached to them.
