Related papers: Irreducible Virasoro modules from tensor products

In this paper, we classify the irreducible Harish-Chandra modules over the full toroidal Lie algebra, which is a natural higher-dimensional analogue of the affine-Virasoro algebra. In particular, we complete the classification of…

We classify the irreducible modules of a rational Lorentzian lattice vertex operator algebra (LLVOA) based on an even, self-dual Lorentzian lattice $\Lambda\subset\mathbb{R}^{m,n}$ of signature $(m,n)$. We show that the set of isomorphism…

In this paper, we studied the jet modules for the centerless Virasoro-like algebra which is the Lie algebra of the Lie group of the area-preserving diffeomorphisms of a $2$-torus. The jet modules are certain natural modules over the Lie…

In this paper, we introduce a new family of functors from the category of modules for the Weyl algebra to the category of modules for the super-Virasoro algebras. The properties of these functors are investigated, with an emphasis on…

Suppose $V^G$ is the fixed-point vertex operator subalgebra of a compact group $G$ acting on a simple abelian intertwining algebra $V$. We show that if all irreducible $V^G$-modules contained in $V$ live in some braided tensor category of…

We study Demazure modules which occur in a level $\ell$ irreducible integrable representation of an affine Lie algebra. We also assume that they are stable under the action of the standard maximal parabolic subalgebra of the affine Lie…

Let $\mathcal{O}_c$ be the category of finite-length central-charge-$c$ modules for the Virasoro Lie algebra whose composition factors are irreducible quotients of reducible Verma modules. Recently, it has been shown that $\mathcal{O}_c$…

Using the fusion product of the representations of the Lie algebra $\mathfrak{sl}_2$ we construct a set of the integrable highest weight $\hat{\mathfrak{sl}_2}$-modules $L^D$, depending on the vector $D\in\mathbb{N}^{k+1}$. In a special…

In this paper, we prove the category of finite length modules for the $\mathbb{Z}_2$-orbifold $M(1)^+$ of the Heisenberg vertex operator algebra whose simple composition factors are $M(1)^\pm$ or $M(1,\lambda)$ for $\lambda \in…

We consider integrable category $\mathcal{O}$ representations of Borcherds--Kac--Moody algebras whose Cartan matrix is finite dimensional, and determine the necessary and sufficient conditions for which the tensor product of irreducible…

Let V be a simple vertex operator algebra satisfying the following conditions: (i) The homogeneous subspaces of V of weights less than 0 are 0, the homogeneous subspace of V of weight 0 is spanned by the vacuum and V' is isomorphic to V as…

For any additive subgroup $G$ of an arbitrary field $F$ of characteristic zero, there corresponds a generalized Heisenberg-Virasoro algebra $L[G]$. Given a total order of $G$ compatible with its group structure, and any…

We first define a class of non-weight modules over the N=1 Heisenberg-Virasoro superalgebra $\mathfrak{g}$, which are reducible modules. Then we give all submodules of such modules, and present the corresponding irreducible quotient modules…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…

We construct explicitly a large family of Gelfand-Tsetlin modules for an arbitrary finite W-algebra of type A and establish their irreducibility. A basis of these modules is formed by the Gelfand-Tsetlin tableaux whose entries satisfy…

We extend the Dong-Mason theorem on the irreducibility of modules for orbifold vertex algebras from [C. Dong, G. Mason, Duke Math. J. 86 (1997)] 305-321] for the category of weak modules. Let $V$ be a vertex operator algebra, $g$ an…

We construct projective covers of irreducible V-modules in the category of grading-restricted generalized V-modules when V is a vertex operator algebra satisfying the following conditions: 1. V is C_{1}-cofinite in the sense of Li. 2. There…

The moduli space $\mathcal M(r,n)$ of framed torsion free sheaves on the projective plane with rank $r$ and second Chern class equal to $n$ has the natural action of the $(r+2)$-dimensional torus. In this paper, we look at the fixed point…

In this paper we completely characterise irreducible tensor products of representations of alternating groups in characteristic 2 of a basic spin module with an irreducible module. This completes the classification of irreducible tensor…

It is well known that using the weight lattice of type $E_6$, $P$, and the lattice construction for vertex operator algebras one can obtain all three level 1 irreducible $\tilde{g}$-modules with $V_P = V^{\Lamba_0} \oplus V^{\Lamba_1}…