The geometry of unitary 2-representations of finite groups and their 2-characters
| dc.creator | Bartlett, Bruce | |
| dc.date | 2008-07-09 | |
| dc.date | 2008-07-21 | |
| dc.date.accessioned | 2026-07-07T09:51:33Z | |
| dc.date.available | 2026-07-07T09:51:33Z | |
| dc.description | Motivated by topological quantum field theory, we investigate the geometric aspects of unitary 2-representations of finite groups on 2-Hilbert spaces, and their 2-characters. We show how the basic ideas of geometric quantization are `categorified' in this context: just as representations of groups correspond to equivariant line bundles, 2-representations of groups correspond to equivariant gerbes. We also show how the 2-character of a 2-representation can be made functorial with respect to morphisms of 2-representations. Under the geometric correspondence, the 2-character of a 2-representation corresponds to the geometric character of its associated equivariant gerbe. This enables us to show that the complexified 2-character is a unitarily fully faithful functor from the complexified homotopy category of unitary 2-representations to the category of unitary equivariant vector bundles over the group. | |
| dc.description | 50 pages, 148 diagrams. Removed two erroneous claims from the introduction, and some minor errors fixed | |
| dc.identifier | https://arxiv.org/abs/0807.1329 | |
| dc.identifier | http://arxiv.org/abs/0807.1329 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165287 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Category Theory | |
| dc.subject | Representation Theory | |
| dc.title | The geometry of unitary 2-representations of finite groups and their 2-characters | |
| dc.type | text |