Related papers: Fusion and the Neveu-Schwarz Singular Vectors
We use recently derived explicit formulae for the Virasoro algebra's singular vectors to give constructive proofs of three results due to Feigin and Fuchs. The main result, which is needed for a rigorous treatment of fusion, describes the…
We derive a set of recursion formulae to construct singular vectors for the $N=2$ (untwisted) algebra, by using the approach of Bauer, di Francesco, Itzykson and Zuber. Applying these formulae, we obtain explicit expressions for the charged…
It was conjectured in arXiv:1211.2788 that bosonization of singular vectors (in Neveu-Schwarz sector) of $\mathcal{N}=1$ super analog of the Virasoro algebra can be identified with Uglov symmetric function. In the paper we prove this…
We write down one-to-one mappings between the singular vectors of the Neveu-Schwarz N=2 superconformal algebra and $16 + 16$ types of singular vectors of the Topological and of the Ramond N=2 superconformal algebras. As a result one obtains…
Using the fusion principle of Bauer et al. we give explicit expressions for some null vectors in the highest weight representations of the \bc algebra in two different forms. These null vectors are the generalization of the Virasoro ones…
In this paper, we give a construction of simple modules generalizing and including both highest weight and Whittaker modules for the Neveu-Schwarz algebra, in the spirit of the work of Mazorchuk and Zhao on simple Virasoro modules. We…
It is shown that the sl(2,C) KZ equation for (half-) integer isospins recovers, up to a gauge transformation, the matrix system for Virasoro algebra singular vectors of Bauer et al. In the case of Kac-Kazhdan spins the general (infinite…
After giving some definitions for vertex operator SUPERalgebras and their modules, we construct an associative algebra corresponding to any vertex operator superalgebra, such that the representations of the vertex operator algebra are in…
The fusion of Verma modules of the osp(1|2) current algebra is studied. In the framework of an isotopic formalism, the singular vector decoupling conditions are analyzed. The fusion rules corresponding to the admissible representations of…
A recent novel derivation of the representation of Virasoro singular vectors in terms of Jack polynomials is extended to the supersymmetric case. The resulting expression of a generic super-Virasoro singular vector is given in terms of a…
The null vectors of an arbitrary highest weight representation of the $WA_2$ algebra are constructed. Using an extension of the enveloping algebra by allowing complex powers of one of the generators, analysed by Kent for the Virasoro…
We calculate explicitly the singular vectors of the Virasoro algebra with the central charge $c\leq 1$. As a result, we have an infinite sequence of the singular vectors for each Fock space with given central charge and highest weight, and…
We give a proof of the conjecture by Belavin, Bershtein and Tarnopolsky, which claims that a bosonization of singular vectors of $N=1$ super Virasoro algebra can be identified with Uglov (Jack $\mathfrak{gl}_p$) symmetric functions with…
We present two explicit expressions for generic singular vectors of type $(r,s)$ of the Virasoro algebra. These results follow from the paper of Bauer et al which presented recursive methods to construct the vectors. The expressions…
We give expressions for the singular vectors in the highest weight representations of the Virasoro algebra. We verify that the expressions --- which take the form of a product of operators applied to the highest weight vector --- do indeed…
Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss…
Explicit expressions for the singular vectors in the highest weight representations of $A_1^{(1)}$ are obtained using the fusion formalism of conformal field theory.
This paper is the third of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we introduce the local von Neumann algebra of the Neveu-Schwarz algebra, to obtain…
This paper is the first of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we present an elementary, progressive and self-contained approch to vertex operator superalgebra.…
We consider exceptional vertex operator algebras for which particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendants of the vacuum. We discuss constraints on these theories that…