Branched Crystals and Category O

V. Chari; D. Jakelic; A. Moura

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arXiv · math/0411582

Branched Crystals and Category O

V. Chari·D. Jakelic·A. Moura

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Abstract

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.

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BibTeX RIS

V. Chari, D. Jakelic, A. Moura. 2004-12-02. Branched Crystals and Category O. https://arxiv.org/abs/math/0411582

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