Bimodule and twisted representation of vertex operator algebras

In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z, we construct an A(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A(M) and intertwining operators. Especially, bimodule A-1T(M) is a natural quotient of A(M) and there is a linear isomorphism between the space IM~k M Mjof intertwining operators and the space of homomorphisms HomA(V)(A(M)  A(V)M~j(s), M~k(t)) for s, t ≤ n, M~j, M~k are g-twisted V modules, if V is g-rational.