Representations of vertex operator algebras and bimodules

TL;DR

This paper constructs and analyzes bimodules associated with vertex operator algebras, exploring their connections to intertwining operators and providing explicit descriptions in the rational case.

Contribution

It introduces a new construction of A_n(V)-bimodules for vertex operator algebras and studies their properties and relations to intertwining operators, especially in rational cases.

Findings

A_n(M) bimodules are explicitly described for rational V.

Connections between A_n(M) and intertwining operators are established.

The structure of bimodules is analyzed for various modules.

Abstract

For a vertex operator algebra V, a V-module M and a nonnegative integer n, an A_n(V)-bimodule A_n(M) is constructed and studied. The connection between A_n(M) and intertwining operators are discussed. In the case that V is rational, A_n(M) for irreducible V-module M is given explicitly.