Symmetric Spaces of Exceptional Groups

Abstract

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.

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

References in corpus (1)

• An introduction to symmetric spaces