Related papers: A proof of the fusion rules theorem
We reconsider the conjecture by Gepner that the fusion ring of a rational conformal field theory is isomorphic to a ring of polynomials in $n$ variables quotiented by an ideal of constraints that derive from a potential. We show that in a…
We introduce intertwining operators among twisted modules or twisted intertwining operators associated to not-necessarily-commuting automorphisms of a vertex operator algebra. Let $V$ be a vertex operator algebra and let $g_{1}$, $g_{2}$…
A cohomological criterion for the complete reducibility of modules of finite length satisfying a composability condition for a meromorphic open-string vertex algebra $V$ has been given by Qi and the author. In order to apply this criterion,…
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…
After giving some definitions for vertex operator SUPERalgebras and their modules, we construct an associative algebra corresponding to any vertex operator superalgebra, such that the representations of the vertex operator algebra are in…
The irreducible modules for the parafermion vertex operator algebra associated to any finite dimensional Lie algebra and any positive integer are identified, the quantum dimensions are computed and the fusion rules are determined.
Here we define a series of associative algebras attached to a vertex operator algebra $V$, called mode transition algebras, showing they reflect both algebraic properties of $V$ and geometric constructions on moduli of curves. One can…
The fusion rule gives the dimensions of spaces of conformal blocks in the WZW theory. We prove a dimension formula similar to the fusion rulefor spaces of coinvariants of affine Lie algebras g^. An equivalence of filtered spaces is…
We prove that higher level Zhu algebras of a vertex operator algebra are isomorphic to subquotients of its universal enveloping algebra.
Working in the axiomatic framework recently proposed by Gaberdiel and Goddard, we prove a generalized version of Zhu's Theorem; for any chiral bosonic conformal field theory on the sphere, our result characterizes the chiral blocks in terms…
This is the third 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…
We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This…
Irreducible modules of the 3-permutation orbifold of a rank one lattice vertex operator algebra are listed explicitly. Fusion rules are determined by using the quantum dimensions. The $S$-matrix is also given.
We extend the modular invariance property of the trace functions of vertex operator algebra on the set of irreducible modules (Zhu's theory) to the case of trace functions of intertwining operators.
In this paper, we use the twisted regular representation theory of vertex operator algebras to construct bimodules over twisted Zhu algebras, extending Haisheng Li's work in untwisted scenarios. Moreover, a conjecture of Dong and Jiang on…
Several aspects of fusion rings and fusion rule algebras, and of their manifestations in twodimensional (conformal) field theory, are described: diagonalization and the connection with modular invariance; the presentation in terms of…
We give a definition of an amenable fusion module over a fusion algebra. A notion of relative integrability for the `coduals' of coideals of compact quantum groups was recently introduced in the joint work of de Commer and Dzokou Talla. We…
This is the first paper of a three-part series in which we develop a theory of conformal blocks for $C_2$-cofinite vertex operator algebras (VOAs) that are not necessarily rational. The ultimate goal of this series is to prove a…
Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…
The purpose of this paper is to generalize Zhu's theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights.…