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

摘要

The double-complex function method suggested in previous papers is extended and the extended method is used to establish two mutually dual extended double Hauser-Ernst equations and related Riemann-Hilbert problems, then quadruple representations of the semidirect product of the Kac-Moody and Virasoro groups are given. These show that, for the stationary axisymmetric vacuum space-times, there are more and richer symmetry structures than previously expected. The multiple forms of some well-known transformations can be obtained as some special cases. (C) 1997 American Institute of Physics. [References: 25]