### Abstract

We give a general theory for the construction of oscillator-like unitary irreducible representations (UIRs) of non-compact supergroups in a super Fock space. This construction applies to all non-compact supergroups G whose coset space G/K with respect to their maximal compact subsupergroup K is "Hermitean supersymmetric". We illustrate our method with the example of SU(m, p/n+q) by giving its oscillator-like UIRs in a "particle state" basis as well as "supercoherent state basis". The same class of UIRs can also be realized over the "super Hilbert spaces" of holomorphic functions of a Z variable labelling the coherent states.

Original language | English (US) |
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Pages (from-to) | 31-51 |

Number of pages | 21 |

Journal | Communications In Mathematical Physics |

Volume | 91 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 1983 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Bars, I., & Günaydin, M. (1983). Unitary representations of non-compact supergroups.

*Communications In Mathematical Physics*,*91*(1), 31-51. https://doi.org/10.1007/BF01206048