Related papers: Z-graded weak modules and regularity

In this paper, given a module $W$ for a vertex operator algebra $V$ and a nonzero complex number $z$ we construct a canonical (weak) $V\otimes V$-module ${\cal{D}}_{P(z)}(W)$ (a subspace of $W^{*}$ depending on $z$). We prove that for…

We continue the study of the vertex operator algebra $L(k,0)$ associated to a type $G_2^{(1)}$ affine Lie algebra at admissible one-third integer levels, $k = -2 + m + \tfrac{i}{3}\ (m\in \mathbb{Z}_{\ge 0}, i = 1,2)$, initiated in…

We give a full classification, in terms of periodic skew diagrams, of irreducible semisimple modules in category O for the degenerate double affine Hecke algebra of type A which can be realized as submodules of Verma modules.

In this paper, we study the endomorphism properties of vertex operator algebras over an arbitrary field $\mathbb{F}$, with $\text{Char}(\mathbb{F}) \neq 2$. Let $V$ be a strongly finitely generated vertex operator algebra over $\mathbb{F}$,…

Graded Hecke algebras can be constructed in terms of equivariant cohomology and constructible sheaves on nilpotent cones. In earlier work, their standard modules and their irreducible modules where realized with such geometric methods. We…

For a rational and $C_2$-cofinite vertex operator algebra $V$ with an automorphism group $G$ of prime order, the fusion rules for twisted $V$-modules are studied, a twisted Verlinde formula which relates fusion rules for $g$-twisted modules…

In this paper, we classify all simple weight modules with finite-dimensional weight spaces over the $N=2$ Ramond algebra. Any such module $V$ is either a simple highest weight module or a simple lowest weight module, or a simple cuspidal…

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…

We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We…

Let A be a noetherian AS regular Koszul quiver algebra (if A is commutative, it is essentially a polynomial ring), and grA the category of finitely generated graded left A-modules. Following Jorgensen, we define the Castelnuovo-Mumford…

Let ${\mathscr M}(p)$ $(p=2,3,\ldots)$ be the singlet vertex operator algebra and $\omega$ its conformal vector. We classify the simple weak ${\mathscr M}(p)$-modules with a non-zero element $u$ such that for some integer $s\geq 2$,…

We define the notion of {\it strongly interlocked} for indecomposable generalized modules for a vertex operator algebra, and show that the notion of graded pseudo-trace is well defined for modules which satisfy this property in certain…

In this paper, we define differential graded vertex operator algebras and the algebraic structures on the associated Zhu algebras and $C_2$-algebras. We also introduce the corresponding notions of modules, and investigate the relations…

Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the kernel of the representation of the modular group on twisted conformal blocks associated…

Let G be a simple, simply connected and connected algebraic group over an algebraically closed field of characteristic p>0, and let V be a rational G-module such that dim V <= p. According to a result of Jantzen, V is completely reducible,…

Given a vertex operator algebra $V$, one can construct two associative algebras, the Zhu algebra $A(V)$ and the $C_2$-algebra $R(V)$. This gives rise to two abelian categories $A(V)-\text{Mod}$ and $R(V)-\text{Mod}$, in addition to the…

Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity $\Theta_{1}\Theta_{2}\Theta_{1}=\Theta_{1}$ instead of anticommutativity) are introduced and their properties are studied. They are described in…

A two-dimensional chiral conformal field theory can be viewed mathematically as the representation theory of its chiral algebra, a vertex operator algebra. Vertex operator algebras are especially well suited for studying logarithmic…

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…

We prove an explicit condition on the level $k$ for the irreducibility of a vacuum module $V^{k}$ over a (non-twisted) affine Lie superalgebra, which was conjectured by M. Gorelik and V.G. Kac. An immediate consequence of this work is the…