Integrability of One-Parameter Groups Generated by the Virasoro Operators

Local one-parameter groups generated by the Virasoro operators were constructed via Feynman path integrals on a coadjoint of the infinite-dimensional Heisenberg group in the previous paper [T. Hashimoto, 1996.J. Funct. Anal.137, 191–218]. The main purpose of this paper is to prove that the one-parameter groups satisfy the integrability condition, i.e., the actions of the one-parameter subgroups are compatible with the action of the Virasoro algebra.