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An analog of the minimal unitary series representations for the deformed Virasoro algebra is constructed using vertex operators of the quantum affine algebra $U_q(\hat{sl}_2)$. A similar construction is proposed for the elliptic algebra…
It is known that the Takahashi--Tanimoto identity-based solution in open string field theory derives a kinetic operator which is a sum of twisted Virasoro generators. Applying the infinite circumstance description of conformal field theory,…
In this work, we construct a representation of the Virasoro algebra in the canonical Hilbert space associated to Liouville conformal field theory. The study of the Virasoro operators is performed through the introduction of a new family of…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
In this paper, we construct the Virasoro type additional symmetries of a kind of constrained multi-component KP hierarchy and give the Virasoro flow equation on eigenfunctions and adjoint eigenfunctions. It can also be seen that the…
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…
A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various…
By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the $\mathfrak{bms}_{3}$ algebra are obtained from the Virasoro algebra. We extend this result to construct new families of…
We propose to take a look at a new approach to the study of integral polyhedra. The main idea is to give an integral representation, or matrix model representation, for the key combinatorial characteristics of integral polytopes. Based on…
A new set of realizations of the Virasoro algebra on a bosonic Fock space are found by explicitly computing the Virasoro representations associated with coadjoint orbits of the form (Diff S1) / S1. Some progress is made in understanding the…
For an arbitrary calibrated Frobenius manifold, we construct an infinite dimensional Lie algebra, called the Virasoro-like algebra, which is a deformation of the Virasoro algebra of the Frobenius manifold. By using the Virasoro-like algebra…
Generalized Virasoro algebras (defined as the universal central extension of some generalized Witt algebras) and super-Virasoro algebras and modules of the intermediate series are studied and discussed.
The Hodge tau-function is a generating function for the linear Hodge integrals. It is also a tau-function of the KP hierarchy. In this paper, we first present the Virasoro constraints for the Hodge tau-function in the explicit form of the…
The Virasoro master equation (VME) describes the general affine-Virasoro construction $T=L^{ab}J_aJ_b+iD^a \dif J_a$ in the operator algebra of the WZW model, where $L^{ab}$ is the inverse inertia tensor and $D^a $ is the improvement…
We construct collective field theories associated with one-matrix plus $r$ vector models. Such field theories describe the continuum limit of spin Calogero Moser models. The invariant collective fields consist of a scalar density coupled to…
Operator product expansion (OPE) of two operators in two-dimensional conformal field theory includes a sum over Virasoro descendants of other operator with universal coefficients, dictated exclusively by properties of the Virasoro algebra…
In the present contribution, I report on certain {\it non-linear} and {\it non-local} extensions of the conformal (Virasoro) algebra. These so-called $V$-algebras are matrix generalizations of $W$-algebras. First, in the context of…
A new rigorous approach to conformal field theory is presented. The basic objects are families of complex-valued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of…
Conformal algebra is an axiomatic description of the operator product expansion of chiral fields in conformal field theory. On the other hand, it is an adequate tool for the study of infinite-dimensional Lie algebras satisfying the locality…
In this article, the Virasoro-type reduction and the corresponding inverse reductions are established for W-algebras associated with classical Lie type and nilpotent orbits of height two. Moreover, these results are lifted to the universal…