Related papers: On Exceptional Vertex Operator (Super) Algebras

This paper studies restricted modules of gap-$p$ Virasoro algebra $\L$ and their intrinsic connection to twisted modules of certain vertex algebras. We first establish an equivalence between the category of restricted $\L$-modules of level…

We show that the support of a simple weight module over the Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are infinite dimensional.…

We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…

We analyse the highest weight representations of the N=1 Ramond algebra and show that their structure is richer than previously suggested in the literature. In particular, we show that certain Verma modules over the N=1 Ramond algebra…

Under a suitable hypothesis, we construct a full set of pairwise orthogonal maximal vectors in $V^{\otimes n}$, where $V=V(1)$ is the simple module of highest weight $1$ for the quantized enveloping algebra $\mathbf{U}(\mathfrak{sl}_2)$. We…

The irreducible modules for the fixed point vertex operator subalgebra V_L^+ of the vertex operator algebra V_L associated to an arbitrary positive definite even lattice L under the automorphism lifted from the -1 isometry of L are…

A notion of intermediate vertex subalgebras of lattice vertex operator algebras is introduced, as a generalization of the notion of principal subspaces. Bases and the graded dimensions of such subalgebras are given.As an application, it is…

We study the properties of level zero modules over quantized affine algebras. The proof of the conjecture on the cyclicity of tensor products by Akasaka and the present author is given. Several properties of modules generated by extremal…

We investigate the representations of a class of conformal Galilei algebras in one spatial dimension with central extension. This is done by explicitly constructing all singular vectors within the Verma modules, proving their completeness…

We show that if every module W for a vertex operator algebra V satisfies the condition that the dimension of W/C_1(W) is less than infinity, where C_1(W) is the subspace of W spanned by elements of the form u_{-1}w for u in V of positive…

For a finitely-generated vertex operator algebra of central charge c, a locally convex topological completion is constructed. We construct on the completion a structure of an algebra over the operad of the c/2-th power of the determinant…

The algebra generated by the down and up operators on a differential partially ordered set (poset) encodes essential enumerative and structural properties of the poset. Motivated by the algebras generated by the down and up operators on…

We consider irreducible lowest-weight representations of Cherednik algebras associated to certain classes of complex reflection groups in characteristic p. In particular, we study maximal graded submodules of Verma modules associated to…

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 irreducible representations for the Lie algebra of vector fields on a 2-dimensional torus constructed using the generalized Verma modules. We show that for a certain choice of parameters these representations remain irreducible…

Given a finite-dimensional complex simple Lie algebra $\mathfrak{g}$ and a complex number $\kappa$, let $V^{\kappa}(\mathfrak{g})$ be the associated universal affine vertex algebra. In [GK07], the authors gave a sufficient and necessary…

In this paper we face the study of the representations of the exceptional Lie superalgebra E(5,10). We recall the construction of generalized Verma modules and give a combinatorial description of the restriction to sl_5 of the Verma module…

Herein we study conformal vectors of a Z-graded vertex algebra of (strong) CFT type. We prove that the full vertex algebra automorphism group transitively acts on the set of the conformal vectors of strong CFT type if the vertex algebra is…

The Nekrasov partition function in supersymmetric quantum gauge theory is mathematically formulated as an equivariant integral over certain moduli spaces of sheaves on a complex surface. In ``Seiberg-Witten Theory and Random Partitions'',…

We classify all simple $W_n$-modules with finite-dimensional weight spaces. Every such module is either of a highest weight type or is a quotient of a module of tensor fields on a torus, which was conjectured by Eswara Rao. This generalizes…