A ] 1 9 A ug 1 99 9 Regular representations of vertex operator algebras , I

In a previous study [Li3], the physical super selection principle in vertex operator algebra theory seems to tell us that for a vertex operator algebra V , one should be able to obtain each irreducible V -module from the adjoint module V by changing certain things. To a certain extent, what we are expecting is an analogue of the orbital construction of representations for a Lie group [Ki]. This was our original motivation for this study on regular representations of vertex operator algebras. This is the first paper in a series for this study. In this paper, given a module W for a vertex operator algebra V and a nonzero complex number z we construct a canonical (weak) V ⊗V -module DP (z)(W ) (a subspace of W ∗ depending on z). We prove that for V modules W,W1 and W2, a P (z)-intertwining map of type (