The Riemann–Hilbert transformation for an approach to a representation of the Virasoro group.

In this paper, it is the intent to apply the Riemann–Hilbert transformation developed by Hauser and Ernst [J. Math. Phys. 21, 1126, 1418 (1980)] in providing a new representation of the Virasoro group. It is found that the Geroch group that acts on the solution space of the Einstein field equations is extended to the semidirect product of the Virasoro and Kac–Moody groups; also, the relationship between the infinitesimal transformation given previously [B. Y. Hou and W. Li, Lett. Math. Phys. 13, 1 (1987); J. Phys. A 20, L897 (1987); W. Li, Phys. Lett. A 129, 301 (1988)] and the infinitesimal Riemann–Hilbert transformation is pointed out. Finally, it is shown that the well-known Neugebauer–Backlund transformation can be derived from the Riemann–Hilbert transformation. [ABSTRACT FROM AUTHOR]