Gerbes on complex reductive Lie groups
| dc.creator | Brylinski, Jean-Luc | |
| dc.date | 2000-02-19 | |
| dc.date.accessioned | 2026-07-07T04:33:58Z | |
| dc.date.available | 2026-07-07T04:33:58Z | |
| dc.description | We construct a gerbe over a complex reductive Lie group G attached to an invariant bilinear form on a maximal diagonalizable subalgebra which is Weyl group invariant and satisfies a parity condition. By restriction to a maximal compact subgroup K, one then gets a gerbe over K. For a simply-connected group, the parity condition is the same used by Pressley and Segal; in general, it was introduced by Deligne and the author. The gerbe is defined by geometric methods, using the so-called Grothendieck manifold. It is equivariant under the conjugation action of G; its restriction to a semisimple orbit is not always trivial. The paper starts with a discussion of gerbe data (in the sense of Chatterjee and Hitchin) and of gerbes as geometric objects (sheaves of groupoids); the relation between the two approaches is presented. There is an Appendix on equivariant gerbes, discussed from both points of view. | |
| dc.description | 33 pages; plain tex | |
| dc.identifier | https://arxiv.org/abs/math/0002158 | |
| dc.identifier | http://arxiv.org/abs/math/0002158 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58725 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 22E46, 14L30, 81T30, 20L05, 53C05 | |
| dc.title | Gerbes on complex reductive Lie groups | |
| dc.type | text |