The geometry of unitary 2-representations of finite groups and their 2-characters
| dc.contributor.author | Bartlett, Bruce | |
| dc.date.accessioned | 2013-01-31T14:06:16Z | |
| dc.date.available | 2013-01-31T14:06:16Z | |
| dc.date.issued | 2011-02 | |
| dc.description | The original publication is available at http://link.springer.com/journal/10485 | en_ZA |
| dc.description.abstract | 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 tomorphisms 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 Grothendieck category of unitary 2-representations to the category of unitary conjugation equivariant vector bundles over the group. | en_ZA |
| dc.description.version | Post-print | en_ZA |
| dc.format.extent | 50 p. | |
| dc.identifier.citation | Bartlett, B. 2011. The Geometry of Unitary 2-Representations of Finite Groups and their 2-Characters. Applied categorical Structures, 19(1): 175-232, doi:10.1007/s10485-009-9189-0. | en_ZA |
| dc.identifier.issn | 1572-9095 (Online) | |
| dc.identifier.issn | 0927-2852 (Print) | |
| dc.identifier.issn | doi:10.1007/s10485-009-9189-0 | |
| dc.identifier.uri | http://hdl.handle.net/10019.1/79319 | |
| dc.language.iso | en_ZA | en_ZA |
| dc.publisher | Springer Link | en_ZA |
| dc.rights.holder | Springer Science + Business Media B.V. | en_ZA |
| dc.subject | 2-Category | en_ZA |
| dc.subject | Unitary 2-representation | en_ZA |
| dc.subject | 2-Character | en_ZA |
| dc.subject | Geometric quantization | en_ZA |
| dc.subject | Adjunction | en_ZA |
| dc.subject | Equivariant gerbe | en_ZA |
| dc.subject | Unitary groups | en_ZA |
| dc.title | The geometry of unitary 2-representations of finite groups and their 2-characters | en_ZA |
| dc.type | Article | en_ZA |