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October 2013 Magic coset decompositions
Sergio L. Cacciatori, Bianca L. Cerchiai, Alessio Marrani
Adv. Theor. Math. Phys. 17(5): 1077-1128 (October 2013).


By exploiting a "mixed" non-symmetric Freudenthal-Rozenfeld-Tits magic square, two types of coset decompositions are analyzed for the non-compact special Kähler symmetric rank-3 coset $E_{7(-25)}/ [(E_{6(-78)} \times U(1)) / \mathbb{Z}_3]$, occurring in supergravity as the vector multiplets'scalar manifold in $\mathcal{N} = 2, \mathcal{D} = 4$ exceptional Maxwell-Einstein theory. The first decomposition exhibits maximal manifest covariance, whereas the second (triality-symmetric) one is of Iwasawa type, with maximal $SO(8)$ covariance. Generalizations to conformal non-compact, real forms of nondegenerate, simple groups "of type E7" are presented for both classes of coset parametrizations, and relations to rank-3 simple Euclidean Jordan algebras and normed trialities over division algebras are also discussed.


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Sergio L. Cacciatori. Bianca L. Cerchiai. Alessio Marrani. "Magic coset decompositions." Adv. Theor. Math. Phys. 17 (5) 1077 - 1128, October 2013.


Published: October 2013
First available in Project Euclid: 21 August 2014

zbMATH: 1295.81135
MathSciNet: MR3262520

Rights: Copyright © 2013 International Press of Boston


Vol.17 • No. 5 • October 2013
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