Lie Superalgebras, Clifford Algebras, Induced Modules and Nilpotent Orbits
| dc.creator | Musson, Ian M. | |
| dc.date | 2004-02-05 | |
| dc.date | 2004-12-23 | |
| dc.date.accessioned | 2026-07-07T05:05:11Z | |
| dc.date.available | 2026-07-07T05:05:11Z | |
| dc.description | Let $\FRAK{g}$ be a classical simple Lie superalgebra. To every nilpotent orbit $\cal O$ in $\FRAK{g}_0$ we associate a Clifford algebra over the field of rational functions on $\cal O$. We find the rank, $k(\cal O)$ of the bilinear form defining this Clifford algebra, and deduce a lower bound on the multiplicity of a $U(\FRAK{g})$-module with $\cal O$ or an orbital subvariety of $\cal O$ as associated variety. In some cases we obtain modules where the lower bound on multiplicity is attained using parabolic induction. The invariant $k(\cal O)$ is in many cases, equal to the odd dimension of the orbit $G\cdot\cal O$ where $G$ is a Lie supergroup with Lie superalgebra ${\mathfrak g.}$ | |
| dc.description | Accepted for publication in Advances in Mathematics. Some minor changes have been made to the original version, mostly in the last section | |
| dc.identifier | https://arxiv.org/abs/math/0402089 | |
| dc.identifier | http://arxiv.org/abs/math/0402089 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70079 | |
| dc.subject | Representation Theory | |
| dc.subject | 17B35 | |
| dc.title | Lie Superalgebras, Clifford Algebras, Induced Modules and Nilpotent Orbits | |
| dc.type | text |