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.
ASJC Scopus subject areas