Related papers: Positive energy representations of affine vertex a…
In this paper we construct a class of new irreducible modules over untwisted affine Kac-Moody algebras $\widetilde{\mathfrak{g}}$, generalizing and including both highest weight modules and Whittaker modules. These modules allow us to…
We shall first present an explicit realization of the simple $N=4$ superconformal vertex algebra $L_{c} ^{N=4}$ with central charge $c=-9$. This vertex superalgebra is realized inside of the $ b c \beta \gamma $ system and contains a…
The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper we consider the general set-up of a vertex algebra $V$, graded by $\G/\Z$ for some…
This paper is a natural continuation of our previous work on conformal embeddings of vertex algebras [6], [7], [8]. Here we consider conformal embeddings in simple affine vertex superalgebra $V_k(\mathfrak g)$ where $\mathfrak g=\mathfrak…
We show that the Hopf link invariants for an appropriate set of finite dimensional representations of $ U_q SL(2)$ are identical, up to overall normalisation, to the modular S matrix of Kac and Wakimoto for rational $k$ $\widehat {sl(2)}$…
Given a group \( G \), a field \( \kappa \), and a factor set \( \sigma \) arising from a partial projective \( \kappa \)-representation of \( G \). This leads to the construction of a topological partial dynamical system \( (\Omega_\sigma,…
In this paper we study general highest weight modules $\mathbb{V}^\lambda$ over a complex finite-dimensional semisimple Lie algebra $\mathfrak{g}$. We present three formulas for the set of weights of a large family of modules…
We study the representation theory of the superconformal algebra $W_k(g,f_{\theta})$ associated with a minimal gradation of $g$. Here, $g$ is a simple finite-dimensional Lie superalgebra with a non-degenerate, even supersymmetric invariant…
(Affine) $\mathcal{W}$-algebras are a family of vertex algebras defined by the generalized Drinfeld-Sokolov reductions associated with a finite-dimensional reductive Lie algebra $\mathfrak{g}$ over $\mathbb{C}$, a nilpotent element $f$ in…
We construct vertex operator representations for the full (N+1)-toroidal Lie algebra g. We associate with g a toroidal vertex operator algebra, which is a tensor product of an affine VOA, a sub-VOA of a hyperbolic lattice VOA, affine sl(N)…
We apply the general theory of tensor products of modules for a vertex operator algebra developed in our papers hep-th/9309076, hep-th/9309159, hep-th/9401119, q-alg/9505018, q-alg/9505019 and q-alg/9505020 to the case of the…
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,…
This is the third of a series of articles devoted to the study of relaxed highest weight modules over vertex operator algebras. Relaxed highest weight modules over affine vertex algebras associated to higher rank Lie algebras $A_\ell$ are…
Let $\fg$ be a simple finite-dimensional complex Lie algebra with a Cartan subalgebra $\fh$ and Weyl group $W$. Let $\fg_n$ denote the Lie algebra of $n$-jets on $\fg$. A theorem of Rais and Tauvel and Geoffriau identifies the centre of the…
Affine Toda theories with imaginary couplings associate with any simple Lie algebra ${\bf g}$ generalisations of Sine Gordon theory which are likewise integrable and possess soliton solutions. The solitons are \lq\lq created" by…
Let $\mathcal{V}^c(\mathfrak{gl}_N)$ be Etingof--Kazhdan's quantum affine vertex algebra associated with the trigonometric $R$-matrix. We establish a connection between suitably generalized deformed $\phi$-coordinated…
We study modularity of the characters of a vertex (super)algebra equipped with a family of conformal structures. Along the way we introduce the notions of rationality and cofiniteness relative to such a family. We apply the results to…
We show that the normalized supercharacters of principal admissible modules over the affine Lie superalgebra $\hat{s\ell}_{2|1}$ (resp. $\hat{ps\ell}_{2|2}$) can be modified, using Zwegers' real analytic corrections, to form a modular…
We give a systematic construction of the symmetries, or observables in the vacuum sector, of a full conformal field theory on an arbitrary real two-dimensional conformal manifold $\Sigma$. Specifically, we construct a prefactorisation…
In this paper, as the first step towards classification of simple weight modules with finite dimensional weight spaces over Witt algebras $W_n$, we explicitly describe supports of such modules. We also obtain some descriptions on the…