The main aim of this paper is to relate almost split sequences to singularity theory by showing that the McKay quiver built from the finite-dimensional representations of a finite subgroup
G
G
of
GL
(
2
,
C
)
\operatorname {GL} (2,{\mathbf {C}})
, where
C
{\mathbf {C}}
is the complex numbers, is isomorphic to the
A
R
AR
quiver of the reflexive modules of the quotient singularity associated with
G
G
.