Related papers: Vertex operator algebras and the Verlinde conjectu…

From a certain induced representation $\mathcal{P}_\ell$ of a double affine Weyl group, we construct a ring $\mathcal{F}_\ell$ that is isomorphic to the fusion ring, or Verlinde algebra, associated to affine Lie algebras at fixed positive…

In this paper, we prove that simple affine vertex operator algebras with positive integral levels admit only trivial first-order deformations. Therefore, the deformation rigidity conjecture of strongly rational vertex operator algebras…

In this paper we study the representations of loop Affine-Virasoro Algebras. As they have canonical triangular decomposition, we define Verma modules and its irreducible quotients. We give necessary and sufficient condition for an…

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…

The vertex operator algebras and modules associated to the highest weight modules for the Virasoro algebra over an arbitrary field F whose characteristic is not equal to 2 are studied. The irreducible modules of vertex operator algebra…

It is proved that the regularity of parafermion vertex operator algebras associated to integrable highest weight modules for affine Kac-Moody algebra A_1^{(1)} implies the C_2-cofiniteness of parafermion vertex operator algebras associated…

Let $V$ be a simple, rational, $C_2$-cofinite vertex operator algebra and $G$ a finite group acting faithfully on $V$ as automorphisms, which is simply called a rational vertex operator algebra with a $G$-action. It is shown that the…

We study a family of non-C2-cofinite vertex operator algebras, called the singlet vertex operator algebras, and connect several important concepts in the theory of vertex operator algebras, quantum modular forms, and modular tensor…

Let $L_{\widehat{osp(1|2)}}(\mathcal{l},0)$ be the simple affine vertex operator superalgebra with admissible level $\mathcal{l}$. We prove that the category of weak $L_{\widehat{osp(1|2)}}(\mathcal{l},0)$-modules on which the positive part…

Haisheng Li showed that given a module (W,Y_W(\cdot,x)) for a vertex algebra (V,Y(\cdot,x)), one can obtain a new V-module W^{\Delta} = (W,Y_W(\Delta(x)\cdot,x)) if \Delta(x) satisfies certain natural conditions. Li presented a collection…

Given a collection of modules of a vertex algebra parametrized by an abelian group, together with one dimensional spaces of composable intertwining operators, we assign a canonical element of the cohomology of an Eilenberg-Mac Lane space.…

We study the meromorphic open-string vertex algebras and their modules over the two-dimensional Riemannian manifolds that are complete, connected, orientable, and of constant sectional curvature $K\neq 0$. Using the parallel tensors, we…

In arXiv:1811.04649, we extended the Dong-Mason theorem on irreducibility of modules for cyclic orbifold vertex algebras to the entire category weak modules and applied this result to Whittaker modules. In this paper we present further…

Fusion rules among irreducible modules of the free bosonic orbifold vertex operator algebra are completely determined.

We show that certain vertex algebras without vacuum vector may be embedded into vertex algebras. The result is a partial analogue of the simple classical fact that any rng can be embedded into a ring. A one-line proof of the case of a…

We give a general, direct and explicit construction of lower-bounded generalized twisted modules satisfying a universal property for a grading-restricted vertex (super)algebra $V$ associated to an automorphism $g$ of $V$. In particular,…

The infinite configuration space of an integrable vertex model based on $U_q\bigl(\hat{gl}(2|2)\bigr)_1$ is studied at $q=0$. Allowing four particular boundary conditions, the infinite configurations are mapped onto the semi-standard…

In this paper, a condition making vertex operator superalgebras to be unitary is determined and an analogue of conformal spin-statistics theorem in conformal field theory is proved. As an application of these results, it is proved that…

Let $G$ be a simple complex Lie group with Lie algebra $\mf g$ and let $\af$ be the affine Lie algebra. We use intertwining operators and Knizhnik-Zamolodchikov equations to construct a family of $\N$-graded vertex operator algebras…

For a vertex operator algebra $V$, we construct an explicit isomorphism between the space of genus-0 conformal blocks associated to permutation-twisted $V^{\otimes n}$-modules and the space of conformal blocks associated to untwisted…