Related papers: Regular representations and $A_{n}(V)$-$A_{m}(V)$ …

We notice that for any positive integer $k$, the set of $(1,2)$-specialized characters of level $k$ standard $A_{1}^{(1)}$-modules is the same as the set of rescaled graded dimensions of the subspaces of level $2k+1$ standard…

Let $V$ be a vector space over a field $F$, $V^*$ its dual space and $L(V)$ the algebra of all linear operators on $V$. For an operator $a\in L(V)$ let $a*$ be its adjoint acting on $V*$, and for a subset $R$ of $L(V)$ let $R"$ be its…

We generalize the main theorem of Rieffel for Morita equivalence of W*-algebras to the case of unital dual operator algebras: two unital dual operator algebras A and B have completely isometric normal representations alpha, beta such that…

Recently Blecher and Kashyap have generalized the notion of W* modules over von Neumann algebras to the setting where the operator algebras are \sigma- weakly closed algebras of operators on a Hilbert space. They call these modules weak*…

For any symmetrizable generalized Cartan matrix $A$, we introduce an algebra $\widehat{\mathcal{DY}}(A)$, which is essentially the centrally extended double Yangian when $A$ is of finite type, and we give a new field (current) presentation…

We consider $AD$-type orbifolds of the triplet vertex algebras $\mathcal{W}(p)$ extending the well-known $c=1$ orbifolds of lattice vertex algebras. We study the structure of Zhu's algebras $A(\mathcal{W}(p)^{A_m})$ and…

Yangian Double $DY(A(m,n))$ of Lie Superalgebra $A(m,n)$ is described in terms of generators and defining relations. It is proved triangular decomposition for Yangian $Y(A(m,n))$ and its quantum double $DY(A(m,n))$ as a corollary of PBW…

We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by 'lowest weight vectors'. We show that such vertex algebras have a 'good' representation theory in the…

A regular vertex operator algebra is a vertex operator algebra such that any weak module (without grading) is a direct sum of ordinary irreducible modules. In this paper we give several sufficient conditions under which a rational vertex…

Let $N_{k} (\g)$ be a vertex operator algebra (VOA) associated to the generalized Verma module for affine Lie algebra of type $A_{\ell -1} ^{(1)}$ or $C_{\ell} ^{(1)}$. We construct a family of ideals $J_{m,n} (\g)$ in $N_{k} (\g)$, and a…

This paper studies the algebraic aspect of a general abelian coset theory with a work of Dong and Lepowsky as our main motivation. It is proved that the vacuum space $\Omega_{V}$ (or the space of highest weight vectors) of a Heisenberg…

Let $V = < p_{ij}(x)e^{\la_ix}, i=1,...,n, j=1, ..., N_i >$ be a space of quasi-polynomials of dimension $N=N_1+...+N_n$. Define the regularized fundamental operator of $V$ as the polynomial differential operator $D = \sum_{i=0}^N…

We show that there are precisely two, up to conjugation, anti-involutions sigma_{\pm} of the algebra of differential operators on the circle preserving the principal gradation. We classify the irreducible quasifinite highest weight…

The {\em superspace ring} of rank $n$ is the algebra $\Omega_n$ of differential forms on affine $n$-space. The algebra $\Omega_n$ is bigraded with respect to polynomial and exterior degree and carries a natural action of the symmetric group…

Let $V$ be a strongly regular vertex operator algebra and let $\frak{ch}_V$ be the space spanned by the characters of the irreducible $V$-modules.\ It is known that $\frak{ch}_V$ is the space of solutions of a so-called \emph{modular linear…

We prove a sharpened version of a conjecture of Dong-Mason about lattice subalgebras of a strongly regular vertex operator algebra $V$, and give some applications. These include the existence of a canonical conformal subVOA $W\otimes…

Let $A_{m,n}$ be the tensor product of the polynomial algebra in $m$ even variables and the exterior algebra in $n$ odd variables over the complex field $\C$, and the Witt superalgebra $W_{m,n}$ be the Lie superalgebra of superderivations…

We study representations of the meromorphic open-string vertex algebra (MOSVAs hereafter) defined in [H3], a noncommutative generalization of vertex (operator) algebra. We start by recalling the definition of a MOSVA $V$ and left…

Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such…

Let $\mathbb K$ be an algebraically closed field of characteristic zero, $A = \mathbb K[x_1,\dots,x_n]$ the polynomial ring, and let $W_n(\mathbb K)$ denote the Lie algebra of all $\mathbb K$-derivations on $A$. The Lie algebra $W_n :=…