%0 Journal Article
%T Branched Crystals and Category O
%A V. Chari
%A D. Jakelic
%A A. Moura
%J Mathematics
%D 2004
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0411582v2