  Let $R$ be a complete local Gorenstein ring of dimension one, with maximal
ideal m. We show that if $M$ is a Cohen-Macaulay $R$-module which begins an
AR-sequence, then this sequence is produced by a particular endomorphism of m
corresponding to a minimal prime ideal. We apply this result to determining the
shape of some components of Auslander-Reiten quivers.
