Bimodules Associated to Twisted Modules of Vertex Operator Algebras and Fusion Rules

Let [Formula: see text] be a vertex operator algebra, [Formula: see text] be in [Formula: see text] and [Formula: see text] for [Formula: see text] be a [Formula: see text]-twisted module, where [Formula: see text] are commuting automorphisms of [Formula: see text] such that [Formula: see text] for [Formula: see text] and [Formula: see text]. Suppose [Formula: see text] is an intertwining operator of type [Formula: see text]. We construct an [Formula: see text]-[Formula: see text]-bimodule [Formula: see text] which determines the action of [Formula: see text] from the bottom level of [Formula: see text] to the bottom level of [Formula: see text], and we explore its connections with fusion rules.