Complex Analysis On Riemann Surfaces Motivated By The Operatorial String Theory

Abstract

This chapter presents a complex analysis on Riemann surfaces motivated by the operatorial string theory. Any multistring diagram determines one and only one meromorphic differential form. All associated algebras are isomorphic to the ordinary Heisenberg and Virasoro algebra. The Riemann analogs of the Fock spaces and Verma modules are isomorphic to the ordinary ones after topological closure. Therefore, there are two filtering structures and one almost-grading structure on the Riemann analogs of Heisenberg and Virasoro algebras. The chapter also presents the realization of the Fock spaces and Verma modules in semi-infinite exterior forms.