### Abstract

E8 algebra constructed as bilinear fermions in the bases of SU(9) and [SU(3)]4 is used to obtain the generators in the bases of the maximal subgroups SO(16), E7×SU(2), and SU(5)×SU(5). The representation of the generators in the Tits subgroup F4×G2 is also obtained using the [SU(3)]4 basis. Simple methods are developed to go from one basis to the other bases. Generators of the exceptional subgroups E7, E6, and F4 are decomposed with respect to their respective Tits subgroups SP(6)×G2, SU(3)×G2, and SO(3)×G2. The possible roles of these subgroups in the symmetry breaking of E8 are merely indicated.

Original language | English |
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Pages (from-to) | 2645-2653 |

Number of pages | 9 |

Journal | Physical Review D |

Volume | 24 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1981 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*24*(10), 2645-2653. https://doi.org/10.1103/PhysRevD.24.2645

**E8 generators as bilinear fermions and its maximal subgroups.** / Koca, Mehmet.

Research output: Contribution to journal › Article

*Physical Review D*, vol. 24, no. 10, pp. 2645-2653. https://doi.org/10.1103/PhysRevD.24.2645

}

TY - JOUR

T1 - E8 generators as bilinear fermions and its maximal subgroups

AU - Koca, Mehmet

PY - 1981

Y1 - 1981

N2 - E8 algebra constructed as bilinear fermions in the bases of SU(9) and [SU(3)]4 is used to obtain the generators in the bases of the maximal subgroups SO(16), E7×SU(2), and SU(5)×SU(5). The representation of the generators in the Tits subgroup F4×G2 is also obtained using the [SU(3)]4 basis. Simple methods are developed to go from one basis to the other bases. Generators of the exceptional subgroups E7, E6, and F4 are decomposed with respect to their respective Tits subgroups SP(6)×G2, SU(3)×G2, and SO(3)×G2. The possible roles of these subgroups in the symmetry breaking of E8 are merely indicated.

AB - E8 algebra constructed as bilinear fermions in the bases of SU(9) and [SU(3)]4 is used to obtain the generators in the bases of the maximal subgroups SO(16), E7×SU(2), and SU(5)×SU(5). The representation of the generators in the Tits subgroup F4×G2 is also obtained using the [SU(3)]4 basis. Simple methods are developed to go from one basis to the other bases. Generators of the exceptional subgroups E7, E6, and F4 are decomposed with respect to their respective Tits subgroups SP(6)×G2, SU(3)×G2, and SO(3)×G2. The possible roles of these subgroups in the symmetry breaking of E8 are merely indicated.

UR - http://www.scopus.com/inward/record.url?scp=35949025382&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35949025382&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.24.2645

DO - 10.1103/PhysRevD.24.2645

M3 - Article

VL - 24

SP - 2645

EP - 2653

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 10

ER -