148 research outputs found

### Introduction to vertex operator algebras I

This is the first part of the revised versions of the notes of three
consecutive expository lectures given by Chongying Dong, Haisheng Li and Yi-Zhi
Huang in the conference on Monster and vertex operator algebras at the Research
Institute of Mathematical Sciences, Kyoto, September 4-9, 1994. In this part we
review the definitions of vertex operator algebras and twisted modules, and
discuss examples.Comment: LaTeX file, 26 page

### Integrability of C_2-cofinite vertex operator algebras

The following integrability theorem for vertex operator algebras V satisfying
some finiteness conditions(C_2-cofinite and CFT-type) is proved: the vertex
operator subalgebra generated by a simple Lie subalgebra {\frak g} of the
weight one subspace V_1 is isomorphic to the irreducible highest weight
\hat{\frak g}-module L(k, 0) for a positive integer k, and V is an integrable
\hat{\frak g}-module. The case in which {\frak g} is replaced by an abelian Lie
subalgebra is also considered, and several consequences of integrability are
discussed.Comment: 13 page

### Representations of vertex operator algebras and bimodules

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.Comment: 17 page

### Unitary vertex operator algebras

Unitary vertex operator algebras are introduced and studied. It is proved
that most well-known rational vertex operator algebras are unitary. The
classification of unitary vertex operator algebras with central charge c less
than or equal to 1 is also discussed.Comment: 31 page

### Classification of irreducible modules for the vertex operator algebra M(1)^+, II: higher rank

The vertex operator algebra M(1)^+ is the fixed point set of free bosonic
vertex operator algebra M(1) under the -1 automorphism. All irreducible modules
for M(1)^+ are classified in this paper for all ranks.Comment: latex, 40 page

### 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

### Modularity in orbifold theory for vertex operator superalgebras

This paper is about the orbifold theory for vertex operator superalgebras.
Given a vertex operator superalgebra V and a finite automorphism group G of V,
we show that the trace functions associated to the twisted sectors are
holomorphic in the upper half plane for any commuting pairs in G under the
C_2-cofinite condition. We also establish that these functions afford a
representation of the full modular group if V is C_2-cofinite and g-rational
for any g in G.Comment: 31 page

### 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

### Twisted representations of vertex operator superalgebras

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, then A_g(V) is finite dimensional semisimple associative algebra
and there are only finitely many irreducible g-twisted V-modules.Comment: 23 page

### Some finite properties for vertex operator superalgebras

Vertex operator superalgebras are studied and various results on rational
Vertex operator superalgebras are obtained. In particular, the vertex operator
super subalgebras generated by the weight 1/2 and weight 1 subspaces are
determined. It is also established that if the even part $V_{\bar 0}$ of a
vertex operator superalgebra $V$ is rational, so is $V.$Comment: 18 page

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