Associating quantum vertex algebras to Lie algebra \gl_{\infty}

In this paper, we present a canonical association of quantum vertex algebras and their $\phi$-coordinated modules to Lie algebra \gl_{\infty} and its 1-dimensional central extension. To this end we construct and make use of another closely related infinite-dimensional Lie algebra.Comment: 22 page

Representations of Z2\mathbb{Z}_{2}-orbifold of the parafermion vertex operator algebra K(sl2,k)K(sl_2,k)

In this paper, the irreducible modules for the $\mathbb{Z}_{2}$-orbifold vertex operator subalgebra of the parafermion vertex operator algebra associated to the irreducible highest weight modules for the affine Kac-Moody algebra $A_1^{(1)}$ of level $k$ are classified and constructed.Comment: 21 page

Bimodules and g-rationality of vertex operator algebras

This paper studies the twisted representations of vertex operator algebras. Let V be a vertex operator algebra and g an automorphism of V of finite order T. For any m,n in (1/T)Z_+, an A_{g,n}(V)-A_{g,m}(V)-bimodule A_{g,n,m}(V) is constructed. The collection of these bimodules determines any admissible g-twisted V-module completely. A Verma type admissible g-twisted V-module is constructed naturally from any A_{g,m}(V)-module. Furthermore, it is shown with the help of bimodule theory that a simple vertex operator algebra V is g-rational if and only if its twisted associative algebra A_g(V) is semisimple and each irreducible admissible g-twisted V-module is ordinary.Comment: 32 page

A characterization of the rational vertex operator algebra VZα+V_{\Z\alpha}^{+}}: II

A characterization of vertex operator algebra $V_L^+$ for any rank one positive definite even lattice $L$ is given in terms of dimensions of homogeneous subspaces of small weights. This result reduces the classification of rational vertex operator algebras of central charge 1 to the characterization of three vertex operator algebras in the $E$-series of central charge one.Comment: 32 page

Representations for the non-graded Virasoro-like algebra

It is proved that an irreducible module over the non-graded Virasoro-like algebra, which satisfies a natural condition, is a GHW module or uniformly bounded. Furthermore, the classification of some uniformly bounded modules is given.Comment: 29 pages

Bimodules associated to vertex operator algebras

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 use A_{n,m}(V) to construct naturally admissible V-modules from A_m(V)-modules. We also determine the structure of A_{n,m}(V) when V is rational.Comment: a minor chang

On a category of gl∞gl_{\infty}-modules

We study a particular category ${\cal{C}}$ of \gl_{\infty}-modules and a subcategory ${\cal{C}}_{int}$ of integrable \gl_{\infty}-modules. As the main results, we classify the irreducible modules in these two categories and we show that every module in category ${\cal{C}}_{int}$ is semi-simple. Furthermore, we determine the decomposition of the tensor products of irreducible modules in category ${\cal{C}}_{int}$.Comment: 26 page

Representations of the vertex operator algebra V_{L_{2}}^{A_{4}}

The rationality and C_2-cofiniteness of the orbifold vertex operator algebra V_{L_{2}}^{A_{4}} are established and all the irreducible modules are constructed and classified. This is part of classification of rational vertex operator algebras with c=1.Comment: 24 pages, a correction of Lemma 5.

A characterization of the vertex operator algebra VL2A4V_{L_{2}}^{A_{4}}

The rational vertex operator algebra $V_{L_{2}}^{A_{4}}$ is characterized in terms of weights of primary vectors. This reduces the classification of rational vertex operator algebras with $c=1$ to the characterizations of $V_{L_{2}}^{S_{4}}$ and $V_{L_{2}}^{A_{5}}.$Comment: 19 pages, published versio

Representations of vertex operator algebras

This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras A_n(V) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V) is a semisimple associative algebra and each irreducible admissible $V$-module is ordinary.Comment: 13 pages, final version for publicatio