New infinite-dimensional quadruple symmetry groups for the general symplectic gravity model

摘要

The symmetry structures of the general symplectic gravity model are further studied. By using the so-called extended double (ED)-complex function method, the usual Riemann-Hilbert (RH) problem is extended to an ED-complex formulation. For any fixed non-negative integer n, two pairs of ED RH transformations are constructed and they are verified to give infinite-dimensional quadruple symmetry groups of the general symplectic gravity model, each of these symmetry groups has the structure of semidirect product of Kac-Moody group Sp(2(n (+) over cap 1),R) and Virasoro group. Moreover, the infinitesimal forms of these RH transformations are calculated out and they are found to give exactly the same results as previous; these demonstrate that the two pairs of ED RH transformations in this paper provide exponentiations of all the infinitesimal symmetries in our previous paper. The finite forms of symmetry transformations given in the present paper are more important and useful for theoretic studies and new solution generation, etc. (C) 2008 American Institute of Physics.