Classification of Irreducible Modules for the Vertex Operator Algebra M(1)+

ct 2 00 2 Classification of irreducible modules for the vertex operator algebra V + L : General case

The irreducible modules for the fixed point vertex operator subalgebra V + L of the vertex operator algebra VL associated to an arbitrary positive definite even lattice L under the automorphism lifted from the −1 isometry of L are classified.

Vertex Operator Algebra Structure of Standard Affine Lie Algebra Modules

Induced modules for vertex operator algebras

For a vertex operator algebra V and a vertex operator subalgebra V ′ which is invariant under an automorphism g of V of finite order, we introduce a g-twisted induction functor from the category of g-twisted V ′-modules to the category of g-twisted V -modules. This functor satisfies the Frobenius reciprocity and transitivity. The results are illustrated with V ′ being the g-invariants in simple...

Twisted modules for vertex operator algebras

In this contribution, I explain the general principles of twisted modules for vertex operator algebras in its powerful formulation using formal series, and derive new general relations satisfied by twisted and non-twisted vertex operators. I prove new “equivalence” and “construction” theorems, identifying a very restricted set of sufficient conditions in order to have a twisted module for a ver...

A logarithmic generalization of tensor product theory for modules for a vertex operator algebra

We describe a logarithmic tensor product theory for certain module categories for a “conformal vertex algebra.” In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. The corresponding intertwining operators contain logarithm...