On the scalar manifold of exceptional supergravity (Q2915775)

In the paper two parametrizations of the non-compact exceptional Lie group \(G = E_{7(-25)}\) are constructed. The parametrizations are based on a fibration which has the maximal compact subgroup \(K\) as a fiber. By making use of the exponential map a realization of \(G/K\) is computed. It provides a basis for the corresponding supergravity theory, which is the analogue of the Calabi-Vesentini coordinates. Then the Iwasawa decomposition is studied. The authors notice that being based on the properties of a ``mixed'' Freudenthal-Tits magic square, the whole procedure can be generalized to a broader class of groups of type \(E_7\).