On the sum of the index of a parabolic subalgebra and of its nilpotent radical
| dc.creator | Yu, Rupert W. T. | |
| dc.date | 2006-06-12 | |
| dc.date | 2006-06-13 | |
| dc.date.accessioned | 2026-07-07T12:34:08Z | |
| dc.date.available | 2026-07-07T12:34:08Z | |
| dc.description | In this short note, we investigate the following question of Panyushev : ``Is the sum of the index of a parabolic subalgebra of a semisimple Lie algebra $\mathfrak{g}$ and the index of its nilpotent radical always greater than or equal to the rank of $\mathfrak{g}$?''. Using the formula for the index of parabolic subalgebras conjectured by Tauvel and the author, and proved by Millet-Fauquant and Joseph, we give a positive answer to this question. Moreover, we also obtain a necessary and sufficient condition for this sum to be equal to the rank of $\mathfrak{g}$. This provides new examples of direct sum decomposition of a semisimple Lie algebra verifying the ``index additivity condition'' as stated by Ra{\"ı}s. | |
| dc.description | Author's affiliation added in the second version | |
| dc.identifier | https://arxiv.org/abs/math/0606268 | |
| dc.identifier | http://arxiv.org/abs/math/0606268 | |
| dc.identifier | Proceedings of the American Mathematical Society 136 (2008) 1515-1522 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217318 | |
| dc.subject | Representation Theory | |
| dc.subject | 17B20 | |
| dc.title | On the sum of the index of a parabolic subalgebra and of its nilpotent radical | |
| dc.type | text |