Related papers: Some applications and constructions of intertwinin…
Fusion product originates in the algebraisation of the operator product expansion in conformal field theory. Read and Saleur (2007) introduced an analogue of fusion for modules over associative algebras, for example those appearing in the…
This is the first of two papers in which we study the modular invariance of pseudotraces of logarithmic intertwining operators. We construct and study genus-one correlation functions for logarithmic intertwining operators among generalized…
Let $L$ be an even (positive definite) lattice and $g\in O(L)$. In this article, we prove that the orbifold vertex operator algebra $V_{L}^{\hat{g}}$ has group-like fusion if and only if $g$ acts trivially on the discriminant group…
We introduce a category B of bounded modules for the toroidal Lie algebras and study irreducible modules in B. We show that one of the irreducible modules in this category, L(T_0), admits a structure of a vertex operator algebra. We prove…
We study a class of representations of the Cuntz algebras O_N, N=2,3,..., acting on L^2(T) where T=R/2\pi Z. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
This paper contains a complete description of minimal non-gatherable triangle triples in the lambda-sequences for the affine classical root systems and some claims for arbitrary (reduced) affine root systems. It continues our previous paper…
The $\mathbb{Z}/2\mathbb{Z}$--graded intertwining operators are introduced. We study these operators in the case of ``degenerate'' N=1 minimal models, with the central charge $c=3/2$. The corresponding fusion ring is isomorphic to the…
The Dunkl operators associated to a dihedral group are a pair of differential-difference operators that generate a commutative algebra acting on differentiable functions in $\mathbb{R}^2$. The intertwining operator intertwines between this…
We study the general twisted intertwining operators (intertwining operators among twisted modules) for a vertex operator algebra $V$. We give the skew-symmetry and contragredient isomorphisms between spaces of twisted intertwining operators…
By a pointed vertex operator algebra (VOA) we mean one whose modules are all simple currents (i.e. invertible), e.g. lattice VOAs. This paper systematically explores the interplay between their orbifolds and tensor category theory. We begin…
First, we prove the Kac-Wakimoto conjecture on modular invariance of characters of exceptional affine W-algebras. In fact more generally we prove modular invariance of characters of all lisse W-algebras obtained through Hamiltonian…
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…
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…
This paper is about the orbifold theory of parafermion vertex operator algebras $K(osp(1|2),k)$ associated to the affine vertex operator superalgebra $L_{\widehat{osp(1|2)}}(k,0)$ with any positive integer $k$. Among the main results, we…
We investigate the representation theory of domestic group schemes $\mathcal{G}$ over an algebraically closed field of characteristic $p > 2$. We present results about filtrations of induced modules, actions on support varieties, Clifford…
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…
The admissible modules for $\hat{sl}_2$ are studied from the point of view of vertex operator algebra. If $l$ is rational such that $l+2={p\over q}$ for some coprime positive integers $p\ge 2$ and $q$, Kac and Wakimoto found finitely many…
We study a vertex operator algebra containing a tensor product of Ising models. It is a direct sum of code vertex operator algebra and its irreducible modules. Therefore, we classify all irreducible modules of code vertex operator algebras…
This paper investigates the representation theory of the algebra of partially transposed permutation operators, $\mathcal{A}^d_{p,p}$, which provides a matrix representation for the abstract walled Brauer algebra. This algebra has recently…