Related papers: Vertex Operators for Deformed Virasoro Algebra
We describe the construction of the quantum deformed affine Lie algebras using the vertex operators in the free field theory. We prove the Serre relations for the quantum deformed Borel subalgebras of affine algebras, namely the case of…
We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We…
These lectures were prepared to be presented at A.A. Belavin seminar on CFT at Landau Institute for Theoretical Physics. We review bosonization of CFT and show how it can be applied to the studying of representations of…
The concept of $\lambda$-differential operators is a natural generalization of differential operators and difference operators. In this paper, we determine the $\lambda$-differential Lie algebraic structure on the Witt algebra and the…
We pursue our study of generalised Kac-Moody and Virasoro algebras defined on compact homogeneous manifolds. Extending the well-known Vertex operator in the case of the two-torus or the two-sphere, we obtain explicit bosonic realisations of…
We obtain explicit expressions for differential operators defining the action of the Virasoro algebra on the space of univalent functions. We also obtain an explicit Taylor decomposition for Schwarzian derivative and a formula for the…
In this paper as a continuation of Part I, the case of two kinds of boson operators is treated. The deformation of the coherent states for the su(2)- and the su(1,1)-algebra and their related deformed algebras are discussed in various forms…
Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…
In this work we give an explicit construction for the vertex operators of massless states in the pure spinor superstring in a plane wave background. The construction is based on the observation that the full action can be divided in two…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
A construction of the Virasoro algebra in terms of free massless two-dimensional boson fields is studied. The ansatz for the Virasoro field contains the most general unitary scaling dimension 2 expression built from vertex operators. The…
Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field…
We revisit the construction of integral forms for vertex (operator) algebras $V_L$ based on even lattices $L$ using generators instead of bases, and we construct integral forms for $V_L$-modules. We construct integral forms for vertex…
The radical of a vertex operator algebra associated to a module is defined and computed.
In a series of papers by Henkel, Roger and Unterberger, Schr\"{o}dinger-Virasoro algebras and their deformations were introduced and investigated. In the present paper we determine the 2-cocycles of a class of deformative…
We show the OPE formulae for three types of deformed super-Virasoro algebras: Chaichian-Presnajder's deformation, Belov-Chaltikhian's one and its modified version. Fundamental (anti-)commutation relations toward a ghost realization of…
The homogeneous Rota-Baxter operators on the Witt and Virasoro algebras are classified. As applications, the induced solutions of the classical Yang-Baxter equation and the induced pre-Lie and PostLie algebra structures are obtained.
The rational vertex operator algebra $V_{L_{2}}^{A_{4}}$ is characterized in terms of weights of primary vectors. This reduces the classification of rational vertex operator algebras with $c=1$ to the characterizations of…
We describe explicitly the vertex algebra of (twisted) chiral differential operators on certain nilmanifolds and construct their logarithmic modules. This is achieved by generalizing the construction of vertex operators in terms of…
We describe a number of relationships between properties of the vacuum Verma module of a Virasoro algebra and the automorphism group of certain vertex operator algebras. These groups include the Deligne exceptional series of simple Lie…