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 is an element of 1/TZ(+), we construct an A(g,n)(V)-bimodule A(g,n)(M) and study its properties, discuss the connections between bimodule A(g,n)(M) and intertwining operators. Especially, bimodule A(g,n-1T) (M) is a natural quotient of A(g,n)(M) and there is a linear isomorphism between the space I-MMj(Mk) of intertwining operators and the space of homomorphisms Hom(Ag,n(V))(A(g,n)(M) circle times A(g,n)(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.