ALGEBRA AND TWISTED ALGEBRA IN TOROIDAL TARGET-SPACE

Target space duality is reconsidered from the viewpoint of quantizatio n in a space with nontrivial topology. An algebra of operators for the toroidal bosonic string is defined and its representations are constr ucted. It is shown that there exist an infinite number of inequivalent quantizations, which are parametrized by two parameters 0 less than o r equal to s, t < 1. The spectrum exhibits the duality only when s = t or -t (mod 1). A deformation of the algebra by a central extension is also introduced. It leads to a kind of twisted relation between the z ero mode quantum number and the topological winding number.