## Abstract

We explore a new direction in representation theory which comes from holomorphic gerbes on complex tori. The analogue of the theta group of a holomorphic line bundle on a (compact) complex torus is developed for gerbes in place of line bundles. The theta group of symmetries of the gerbe has the structure of a Picard groupoid. We calculate it explicitly as a central extension of the group of symmetries of the gerbe by the Picard groupoid of the underlying complex torus. We discuss obstruction to equivariance and give an example of a group of symmetries of a gerbe with respect to which the gerbe cannot be equivariant. We calculate the obstructions to invariant gerbes for some group of translations of a torus to be equivariant. We survey various types of representations of the group of symmetries of a gerbe on the stack of sheaves of modules on the gerbe and the associated abelian category of sheaves on the gerbe (twisted sheaves).

Original language | English |
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Pages (from-to) | 209-221 |

Number of pages | 13 |

Journal | Journal of Geometry and Physics |

Volume | 64 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2013 |

Externally published | Yes |

## Keywords

- Brauer group
- Complex tori
- Gerbes
- Heisenberg group

## ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy (all)
- Geometry and Topology