EXTENDED DOUBLE RIEMANN-HILBERT PROBLEM AND MULTIPLE REPRESENTATIONS OF THE INFINITE-DIMENSIONAL SYMMETRICAL GROUP FOR THE STATIONARY AXISYMMETRICAL VACUUM FIELD-EQUATIONS

The double-complex function method suggested in previous papers is ext ended and the extended method is used to establish two mutually dual e xtended double Hauser-Ernst equations and related Riemann-Hilbert prob lems, then quadruple representations of the semidirect product of the Kac-Moody and Virasoro groups are given. These show that, for the stat ionary axisymmetric vacuum space-times, there are more and richer symm etry structures than previously expected. The multiple forms of some w ell-known transformations can be obtained as some special cases. (C) 1 997 American Institute of Physics.