Symmetric Spaces of Exceptional Groups

Details Symmetric Spaces of Exceptional Groups Symmetric Spaces of Exceptional Groups

2008-11-04

arxiv.org/abs/0811.0554v1

Physics

Mathematical Physics

Presented at the 27th ICGTMP (2008), Yerevan (Armenia)

Scientific paper

We adress the problem of the reasons for the existence of 12 symmetric spaces with the exceptional Lie groups. The 1+2 cases for $G_2$ and $F_4$ respectively are easily explained from the octonionic nature of these groups. The 4+3+2 cases on the $E_{6,7,8}$ series require the magic square of Freudenthal and, for the split case, an appeal to the supergravity chain in $5, 4$ and 3 spacetime dimensions.

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