New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields

The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein--Maxwell theory with p Abelian gauge fields (EM-p theory, for short). Two EHC structural Riemann--Hilbert (RH) transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac--Moody group \widehatSU(p+1,1) and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author's paper by a different scheme. This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.