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Let V be a simple vertex operator algebra and G a finite automorphism group. Then there is a natural right G-action on the set of all inequivalent irreducible V-modules. Let S be a finite set of inequivalent irreducible V-modules which is…
This paper gives an analogue of A_g(V) theory for a vertex operator superalgebra V and an automorphism g of finite order. The relation between the g-twisted V-modules and A_g(V)-modules is established. It is proved that if V is g-rational,…
Let $V$ be a vertex operator algebra and $g$ an automorphism of finite order. We construct an associative algebra $A_g(V)$ and a pair of functors between the category of $A_g(V)$-modules and a certain category of admissible $g$-twisted…
Let V be a vertex operator algebra and m,n be nonnegative integers. We construct an A_n(V)-A_m(V)-bimodule A_{n,m}(V) which determines the action of V from the level m subspace to level n subspace of an admissible V-module. We show how to…
This is a continuation of our work to understand vertex operator algebras using the geometric properties of varieties attached to vertex operator algebras. For a class of vertex operator algebras including affine vertex operator algebras…
We study simple current extensions of tensor products of two vertex operator algebras satisfying certain conditions. We establish the relationship between the fusion rule for the simple current extension and the fusion rule for a tensor…
In this paper, we prove the categories of lower bounded twisted modules of positive integer levels for simple vertex operator algebras associated with affine Lie algebras and general automorphisms are semisimple, using the twisted…
We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
We apply the general theory of tensor products of modules for a vertex operator algebra developed in our papers hep-th/9309076, hep-th/9309159, hep-th/9401119, q-alg/9505018, q-alg/9505019 and q-alg/9505020 to the case of the…
We exhibit a connection between Etingof-Kazhdan's notion of pseudoderivation and a certain construction of simple current modules for a vertex operator algebra and meanwhile we introduce and study a notion of pseudoendomorphism…
Let V be a vertex operator algebra and g an automorphism of order T. We construct a sequence of associative algebras A_{g,n}(V) with n\in\frac{1}{T}\Z nonnegative such that A_{g,n}(V) is a quotient of A_{g,n+1/T}(V) and a pair of functors…
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…
Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V^G-modules which occur as submodules of irreducible V-modules by using intertwining operators for…
Let V be a simple vertex operator algebra satisfying the following conditions: (i) The homogeneous subspaces of V of weights less than 0 are 0, the homogeneous subspace of V of weight 0 is spanned by the vacuum and V' is isomorphic to V as…
In this paper, we show Kazhdan-Lusztig categories, that is, the categories of lower bounded generalized weight modules for certain affine vertex operator superalgebras that are locally finite modules of the underlying finite dimensional Lie…
We construct a direct sum completion $\mathcal{C}_{\oplus}$ of a given braided monoidal category $\mathcal{C}$ which allows for the rigorous treatment of infinite order simple current extensions of vertex operator algebras as seen in…
We study the subalgebra of the lattice vertex operator algebra $V_{\sqrt{2}A_2}$ consisting of the fixed points of an automorphism which is induced from an order 3 isometry of the root lattice $A_2$. We classify the simple modules for the…
Using general principles in 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…
We discuss a recent proof by the author of a general version of the Verlinde conjecture in the framework of vertex operator algebras and the application of this result to the construction of modular tensor tensor category structure on the…