  In this paper we describe a theory of (branched) crystals which is adapted to
the study of representations in the BGG category $\cal O$ and which generalizes
the theory of normal crystals of Kashiwara. In the case of $sl_2$ we show that
one can associate (uniquely up to isomorphism) to every module in $\cal O$ a
branched crystal . We show that the indecomposable modules in \cal O$
correspond to "indecomposable" branched crystals. We also define the tensor
product of these crystals and show that for $sl_2$ the indecomposable
components of the tensor product of branched crystals are the same as the
crystals associated to the indecomposable summands of the tensor product of the
corresponding modules.
