Related papers: $A_{2l}^{(2)}$ at level $-l-\frac{1}{2}$

Let L(n-l+1/2,0) be the vertex operator algebra associated to an affine Lie algebra of type B_l^(1) at level n-l+1/2, for a positive integer n. We classify irreducible L(n-l+1/2,0)-modules and show that every L(n-l+1/2,0)-module is…

Let $L(-{1/2}(l+1),0)$ be the simple vertex operator algebra associated to an affine Lie algebra of type $A_{l}^{(1)}$ with the lowest admissible half-integer level $-{1/2}(l+1)$, for even l. We study the category of weak modules for that…

The category of weight modules $L_k(\mathfrak{sl}_2)\text{-wtmod}$ of the simple affine vertex algebra of $\mathfrak{sl}_2$ at an admissible level $k$ is neither finite nor semisimple and modules are usually not lower-bounded and have…

In this paper, we prove the categories of lower bounded twisted modules of positive integer levels for simple vertex operator algebras associated with affine Lie algebras and general automorphisms are semisimple, using the twisted…

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…

Let $L_{\widehat{sl(2|1)}}(\mathcal{k},0)$ be the simple affine vertex operator superalgebra associated to the affine Lie superalgebra $\widehat{sl(2|1)}$ with admissible level $\mathcal{k}$. We conjecture that…

In this paper, we construct an irreducible vertex module for twisted affine Lie algebra of type A_{2l}^{(2)}.

This paper is to study vertex operator superalgebras which are strongly generated by their weight-$2$ and weight-$\frac{3}{2}$ homogeneous subspaces. Among the main results, it is proved that if such a vertex operator superalgebra $V$ is…

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…

In this paper, we study representations of the vertex operator algebra $L(k,0)$ at one-third admissible levels $k= -5/3, -4/3, -2/3$ for the affine algebra of type $G_2^{(1)}$. We first determine singular vectors and then obtain a…

In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie…

We use the newly developed technique of inverse quantum hamiltonian reduction to investigate the representation theory of the simple affine vertex algebra $\mathsf{A}_{2}(\mathsf{u},2)$ associated to $\mathfrak{sl}_{3}$ at level $\mathsf{k}…

The main result of this paper is a combinatorial description of a basis of standard level 1 module for the twisted affine Lie algebra $A_2^{(2)}.$ This description also gives two new combinatorial identities of G\"ollnitz (or…

Consider a simple Lie algebra $\mathfrak{g}$ and $\overline{\mathfrak{g}}% \subset \mathfrak{g}$ a Levi subalgebra. Two irreducible $\overline{% \mathfrak{g}}$-modules yield isomorphic inductions to $\mathfrak{g}$ when their highest weights…

In this paper, we investigate the theory of $g$-twisted modules for modular $\frac{1}{2}\mathbb{Z}$-graded vertex superalgebras over an algebraically closed field $\mathbb{F}$ of prime characteristic $p>2$. For a…

We provide an explicit combinatorial description of highest weights of simple highest weight modules over the simple affine vertex algebra of type A of admissible level k. For admissible simple highest weight modules corresponding to the…

In this paper we study a series of vertex operator algebras of integer level associated to the affine Lie algebra $A_{\ell}^{(1)}$. These vertex operator algebras are constructed by using the explicit construction of certain singular…

We construct a class of non-weight modules over the twisted $N=2$ superconformal algebra $\T$. Let $\mathfrak{h}=\C L_0\oplus\C G_0$ be the Cartan subalgebra of $\T$, and let $\mathfrak{t}=\C L_0$ be the Cartan subalgebra of even part…

We provide an explicit classification of all simple $\mathfrak{sl}_2$-modules that are torsion free of rank $1$ over the Cartan subalgebra. We also establish a similar result for the first Weyl algebra and for the Lie superalgebra…

In this paper we study the category of graded modules for the current algebra associated to $\mathfrak{sl}_2$. The category enjoys many nice properties, including a tilting theory which was established in previous work of the authors. We…