Related papers: Fusion Rules for the Lattice Vertex Operator Algeb…

In this paper we prove that the vertex algebra $V_L^+$ is rational if $L$ is a negative definite even lattice of finite rank, or if $L$ is a non-degenerate even lattice of a finite rank that is neither positive definite nor negative…

We classify the irreducible modules for the fixed point vertex operator subalgebra V_L^+ of the vertex operator algebra V_L associated to a positive definite even lattice of rank 1 under the automorphism lifted from the -1 isometry of L.

We reformed the tensor product theory of vertex operator algebras developed by Huang and Lepowsky so that we could apply it to all vertex operator algebras satisfying C_2-cofiniteness. We also showed that the tensor product theory develops…

The admissible modules for $\hat{sl}_2$ are studied from the point of view of vertex operator algebra. If $l$ is rational such that $l+2={p\over q}$ for some coprime positive integers $p\ge 2$ and $q$, Kac and Wakimoto found finitely many…

We show that if every module W for a vertex operator algebra V satisfies the condition that the dimension of W/C_1(W) is less than infinity, where C_1(W) is the subspace of W spanned by elements of the form u_{-1}w for u in V of positive…

We introduce a simple, self-dual, rational, and $C_2$-cofinite vertex operator algebra of CFT-type associated with a $\mathbb{Z}_k$-code for $k \ge 2$ based on the $\mathbb{Z}_k$-symmetry among the simple current modules for the parafermion…

A regular vertex operator algebra is a vertex operator algebra such that any weak module (without grading) is a direct sum of ordinary irreducible modules. In this paper we give several sufficient conditions under which a rational vertex…

We prove that the categories of weight modules over the simple $\mathfrak{sl}(2)$ and $\mathcal{N}=2$ superconformal vertex operator algebras at fractional admissible levels and central charges are rigid (and hence the categories of weight…

In this article, we consider permutation orbifold models of $C_2$-cofinite vertex operator algebras of CFT type. We show the $C_2$-cofiniteness of the 2-cyclic permutation orbifold model $(V\otimes V)^{S_2}$ for an arbitrary $C_2$-cofinite…

Let $V$ be a vertex operator algebra, $k$ a positive integer and $\sigma$ a permutation automorphism of the vertex operator algebra $V^{\otimes k}$. In this paper, we determine the fusion product of any $V^{\otimes k}$-module with any…

This paper is about the orbifold theory of affine and parafermion vertex operator algebras. It is known that the parafermion vertex operator algebra $K(sl_2,k)$ associated to the integrable highest weight modules for the affine Kac-Moody…

We revisit the construction of integral forms for vertex (operator) algebras $V_L$ based on even lattices $L$ using generators instead of bases, and we construct integral forms for $V_L$-modules. We construct integral forms for vertex…

Let L be a rank one positive definite even lattice. We prove that a vertex operator algebra (VOA) V_L^+ satisfies the C_2 condition. Here, V_L^+ is a fixed point sub-VOA of the VOA V_L associated with the automorphism lifted from the -1…

For the Klein group $K$ and a positive integr $k$, irreducible modules of the orbifold vertex operator algebra $L_{\widehat{\mathfrak{sl}_2}}(k,0)^{K}$ have been classified and constructed in \cite{JWa}. In this paper, we determine…

A unitary and strongly rational vertex operator algebra (VOA) $V$ is called strongly unitary if all irreducible $V$-modules are unitarizable. A strongly unitary VOA $V$ is called completely unitary if for each unitary $V$-modules $W_1$,…

The main result is that the category of ordinary modules of an affine vertex operator algebra of a simply laced Lie algebra at admissible level is rigid and thus a braided fusion category. If the level satisfies a certain coprime property…

We study properties of a C_2-cofinite vertex operator algebra of CFT type. If it is also rational and V'\cong V, then the rigidity of the tensor category of modules has been proved by Huang. When we treat an irrational C_2-cofinite VOA, the…

In this paper we discuss the structure of the tensor product V'_{\alpha,\beta}\otimes L(c,h) of irreducible module from intermediate series and irreducible highest weight module over the Virasoro algebra. We generalize Zhang's…

We construct vertex algebraic intertwining operators among certain generalized Verma modules for $\widehat{\mathfrak{sl}(2,\mathbb{C})}$ and calculate the corresponding fusion rules. Additionally, we show that under some conditions these…

Let $\tilde{\mathfrak{g}}$ be the affine Lie algebra of type $A_{2l}^{(2)}$. The integrable highest weight $\tilde{\mathfrak{g}}$-module $L(k\Lambda_0)$ called the standard $\tilde{\mathfrak{g}}$-module is realized by a tensor product of…