  In this paper we completely classify all the special Cohen-Macaulay (=CM)
modules corresponding to the exceptional curves in the dual graph of the
minimal resolutions of all two dimensional quotient singularities. In every
case we exhibit the specials explicitly in a combinatorial way. Our result
relies on realizing the specials as those CM modules whose first Ext group
vanishes against the ring R, thus reducing the problem to combinatorics on the
AR quiver; such possible AR quivers were classified by Auslander and Reiten. We
also give some general homological properties of the special CM modules and
their corresponding reconstruction algebras.
