Weighted projective spaces and minimal nilpotent orbits
| dc.creator | Rossi, C. A. | |
| dc.date | 2007-08-13 | |
| dc.date | 2007-11-06 | |
| dc.date.accessioned | 2026-07-07T08:40:22Z | |
| dc.date.available | 2026-07-07T08:40:22Z | |
| dc.description | We investigate (twisted) rings of differential operators on the resolution of singularities of a particular irreducible component of the (Zarisky) closure of the minimal orbit $\bar O_{\mathrm{min}}$ of $\mathfrak{sp}_{2n}$, intersected with the Borel subalgebra $\mathfrak n_+$ of $\mathfrak{sp}_{2n}$, using toric geometry and show that they are homomorphic images of a subalgebra of the Universal Enveloping Algebra (UEA) of $\mathfrak{sp}_{2n}$, which contains the maximal parabolic subalgebra $\mathfrak p$ determining the minimal nilpotent orbit. Further, using Fourier transforms on Weyl algebras, we show that (twisted) rings of well-suited weighted projective spaces are obtained from the same subalgebra. Finally, investigating this subalgebra from the representation-theoretical point of view, we find new primitive ideals and rediscover old ones for the UEA of $\mathfrak{sp}_{2n}$ coming from the aforementioned resolution of singularities. | |
| dc.description | 15 pages; misprints corrected; some terminology mistakes have been corrected | |
| dc.identifier | https://arxiv.org/abs/0708.1714 | |
| dc.identifier | http://arxiv.org/abs/0708.1714 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141354 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13N10 | |
| dc.title | Weighted projective spaces and minimal nilpotent orbits | |
| dc.type | text |