Bimodule and twisted representation of vertex operator algebras

Abstract

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 $n \in \tfrac{1} {T}\mathbb{Z}_ +$, 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 $A_{g,n - \tfrac{1} {T}} (M)$ (M) is a natural quotient of A _g,n (M) and there is a linear isomorphism between the space $\mathcal{I}_{M M^j }^{M^k }$ of intertwining operators and the space of homomorphisms $Hom_{A_{g,n} (V)} \left( {A_{g,n} \left( M \right) \otimes _{A_{g,n} (V)} M^j \left( s \right),M^k \left( t \right)} \right)$ for s, t ⩽ n, M ^j, M ^k are g-twisted V modules, if V is g-rational.