Branched Crystals and Category O
| dc.creator | Chari, V. | |
| dc.creator | Jakelic, D. | |
| dc.creator | Moura, A. | |
| dc.date | 2004-11-25 | |
| dc.date | 2004-12-02 | |
| dc.date.accessioned | 2026-07-07T09:22:38Z | |
| dc.date.available | 2026-07-07T09:22:38Z | |
| dc.description | 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. | |
| dc.description | References added | |
| dc.identifier | https://arxiv.org/abs/math/0411582 | |
| dc.identifier | http://arxiv.org/abs/math/0411582 | |
| dc.identifier | J. Algebra 294 (2005), no. 1, 51--72. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155444 | |
| dc.subject | Representation Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | 17B99 | |
| dc.title | Branched Crystals and Category O | |
| dc.type | text |