Branched Crystals and Category O

Details Branched Crystals and Category O Branched Crystals and Category O

2004-11-25

arxiv.org/abs/math/0411582v2

J. Algebra 294 (2005), no. 1, 51--72.

Mathematics

Representation Theory

References added

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Branched Crystals and Category O does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Branched Crystals and Category O, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Branched Crystals and Category O will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-415081