Symmetric spaces of exceptional groups
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We address the problem of the reasons for the existence of 12 symmetric spaces with the exceptional Lie groups. The 1 + 2 cases for G2 and F4, respectively, are easily explained from the octonionic nature of these groups. The 4 + 3 + 2 cases on the E6,7,8 series require the magic square of Freudenthal and, for the split case, an appeal to the supergravity chain in 5, 4, and 3 space—time dimensions.
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