Related papers: On vertex operator realizations of Jack functions
The notion of vertex operator coalgebra is presented which corresponds to the family of correlation functions of one string propagating in space-time splitting into n strings in conformal field theory. This notion is in some sense dual to…
We propose a classical analogue of the vertex algebra in the context of classical integrable field theories. We use this fundamental notion to describe the auxiliary function of the linear auxiliary problem as a classical vertex operator.…
We construct 2-representations of quantum affine algebras from 2-representations of quantum Heisenberg algebras. The main tool in this construction are categorical vertex operators, which are certain complexes in a Heisenberg…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
We describe the solutions to a family of rotationally symmetric second order partial differential equations in the complex plane that arises from a four-dimensional complex Lie algebra whose spanning set generates the algebra from which…
We establish several operator versions of the classical Aczel inequality. One of operator versions deals with the weighted operator geometric mean and another is related to the positive sesquilinear forms. Some applications including the…
We study the fixed point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. We classify the irreducible modules for the…
In this paper we improve results related to Normalized Jensen Functional for convex functions and Uniformly Convex Functions.
On locally conformally flat manifolds we describe a construction which maps generalised conformal Killing tensors to differential operators which may act on any conformally weighted tensor bundle; the operators in the range have the…
A linear operator $T$ between two lattice-normed spaces is said to be $p$-compact if, for any $p$-bounded net $x_\alpha$, the net $Tx_\alpha$ has a $p$-convergent subnet. $p$-Compact operators generalize several known classes of operators…
In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…
Snakes are analogues of alternating permutations defined for any Coxeter group. We study these objects from the point of view of combinatorial Hopf algebras, such as noncommutative symmetric functions and their generalizations. The main…
In this paper the sum of an orthogonal matrix and an outer product is studied, and a relation between the norms of the vectors forming the outer product and the singular values of the resulting matrix is presented. The main result may be…
The notion of a Levi operator is an operator abstraction of the Levy property of a norm or, more generally of the Levi topology on a locally solid vector lattice. Various aspects of Levi operators have been studied recently by several…
In this paper, mirror extensions of vertex operator algebras is considered via tensor categories. The mirror extension conjecture is proved.
We give an abstract construction, based on the Belavin-Polyakov-Zamolodchikov equations, of a family of vertex operator algebras of rank $26$ associated to the modified regular representations of the Virasoro algebra. The vertex operators…
This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator…
A vertex operator approach for form factors of Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is constructed on the basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and vertex-face transformation. As simple…
In this article, we propose a $p$-adic analogue of complex Hilbert space and consider generalizations of some well-known theorems from functional analysis and the basic study of operators on Hilbert spaces. We compute the $K$-theory of the…
In the last decade, a large amount of research has been concentrated on the operators living on the model space. Asymmetric truncated Toeplitz operators and asymmetric truncated Hankel operators are the natural generalization of truncated…