Induced modules for vertex operator algebras

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...

Some Twisted Modules for Framed Vertex Operator Algebras

Weak modules and logarithmic intertwining operators for vertex operator algebras

We consider a class of weak modules for vertex operator algebras that we call logarithmic modules. We also construct nontrivial examples of intertwining operators between certain logarithmic modules for the Virasoro vertex operator algebra. At the end we speculate about some possible logarithmic intertwiners at the level c = 0. Introduction This work is an attempt to explain an algebraic reform...

Twisted modules for vertex operator algebras and Bernoulli polynomials

Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an arbitrary twisting automorphism. The construction involves the Bernoulli polynomials in a fundamental way. This is explained through results in the general theory of...