caa a22 4500 445378662 CHVBK 20180317143010.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10485-009-9189-0 doi (NATIONALLICENCE)springer-10.1007/s10485-009-9189-0 Bartlett Bruce University of Sheffield, Sheffield, UK aut The Geometry of Unitary 2-Representations of Finite Groups and their 2-Characters [Elektronische Daten] [Bruce Bartlett] 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 Grothendieck category of unitary 2-representations to the category of unitary conjugation equivariant vector bundles over the group. Springer Science+Business Media B.V., 2009 2-Category nationallicence Unitary 2-representation nationallicence 2-Character nationallicence Geometric quantization nationallicence Adjunction nationallicence Equivariant gerbe nationallicence Applied Categorical Structures Springer Netherlands 19/1(2011-02-01), 175-232 0927-2852 19:1<175 2011 19 10485 https://doi.org/10.1007/s10485-009-9189-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-009-9189-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bartlett Bruce University of Sheffield, Sheffield, UK aut NATIONALLICENCE 773 0- Applied Categorical Structures Springer Netherlands 19/1(2011-02-01), 175-232 0927-2852 19:1<175 2011 19 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer