### Abstract

We give a general bosonic construction of oscillator-like unitary irreducible representations (UIR) of non-compact groups whose coset spaces with respect to their maximal compact subgroups are Hermitian symmetric. With the exception of E_{7(7)}, they include all the non-compact invariance groups of extended supergravity theories in four dimensions. These representations have the remarkable property that each UIR is uniquely determined by an irreducible representation of the maximal compact subgroup. We study the connection between our construction, the Hermitian symmetric spaces and the Tits-Koecher construction of the Lie algebras of corresponding groups. We then give the bosonic construction of the Lie algebra of E_{7(7)} in SU(8), SO(8) and U(7) bases and study its properties. Application of our method to E_{7(7)} leads to reducible unitary representations.

Original language | English (US) |
---|---|

Pages (from-to) | 159-179 |

Number of pages | 21 |

Journal | Communications In Mathematical Physics |

Volume | 87 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 1982 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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*Communications In Mathematical Physics*, vol. 87, no. 2, pp. 159-179. https://doi.org/10.1007/BF01218560

**Oscillator-like unitary representations of non-compact groups with a jordan structure and the non-compact groups of supergravity.** / Günaydin, M.; Saçlioglu, C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Oscillator-like unitary representations of non-compact groups with a jordan structure and the non-compact groups of supergravity

AU - Günaydin, M.

AU - Saçlioglu, C.

PY - 1982/6/1

Y1 - 1982/6/1

N2 - We give a general bosonic construction of oscillator-like unitary irreducible representations (UIR) of non-compact groups whose coset spaces with respect to their maximal compact subgroups are Hermitian symmetric. With the exception of E7(7), they include all the non-compact invariance groups of extended supergravity theories in four dimensions. These representations have the remarkable property that each UIR is uniquely determined by an irreducible representation of the maximal compact subgroup. We study the connection between our construction, the Hermitian symmetric spaces and the Tits-Koecher construction of the Lie algebras of corresponding groups. We then give the bosonic construction of the Lie algebra of E7(7) in SU(8), SO(8) and U(7) bases and study its properties. Application of our method to E7(7) leads to reducible unitary representations.

AB - We give a general bosonic construction of oscillator-like unitary irreducible representations (UIR) of non-compact groups whose coset spaces with respect to their maximal compact subgroups are Hermitian symmetric. With the exception of E7(7), they include all the non-compact invariance groups of extended supergravity theories in four dimensions. These representations have the remarkable property that each UIR is uniquely determined by an irreducible representation of the maximal compact subgroup. We study the connection between our construction, the Hermitian symmetric spaces and the Tits-Koecher construction of the Lie algebras of corresponding groups. We then give the bosonic construction of the Lie algebra of E7(7) in SU(8), SO(8) and U(7) bases and study its properties. Application of our method to E7(7) leads to reducible unitary representations.

UR - http://www.scopus.com/inward/record.url?scp=0002471984&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002471984&partnerID=8YFLogxK

U2 - 10.1007/BF01218560

DO - 10.1007/BF01218560

M3 - Article

AN - SCOPUS:0002471984

VL - 87

SP - 159

EP - 179

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -