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Magic coset decompositions for groups of type E7
Mathematical Physics Seminar| Speaker: | Bianca Letizia Cerchiai, Milano University |
| Location: | 2112 MSB |
| Start time: | Tue, Apr 24 2012, 4:10PM |
By exploiting a "mixed" non-symmetric Freudenthal-Rozenfeld-Tits magic square and using the formalism of Jordan algebras, two types of coset decompositions are analyzed for the non-compact special Kähler symmetric rank-3 coset E7(-25)/[(E6(-78) x U(1))/Z_3], occurring in supergravity as the vector multiplets' scalar manifold in N=2, D=4 exceptional Maxwell-Einstein theory. The first decomposition exhibits the maximal manifest [E6(-78) x U(1)] covariance and is the analogue of a Calabi-Vesentini basis, whereas the second is based on the Iwasawa decomposition, and is triality symmetric with manifest SO(8) covariance. Generalizations to minimally non-compact, real forms of non-degenerate, simple groups "of type E7" are presented.