相关论文: Vertex-IRF transformations and quantization of dyn…

We review some of the recent developments in two dimensional statistical mechanics in which corner transfer matrices provide the vital link between the physical system and the representation theory of quantum affine algebras. This opens…

Deformed gauge transformations on deformed coordinate spaces are considered for any Lie algebra. The representation theory of this gauge group forces us to work in a deformed Lie algebra as well. This deformation rests on a twisted Hopf…

This paper is a continuation of "Quantization of Lie bialgebras I-IV". The goal of this paper is to define and study the notion of a quantum vertex operator algebra in the setting of the formal deformation theory and give interesting…

We use the $q$-characters to compute explicit expressions of the $R$-matrices for first fundamental representations of all types of twisted quantum affine algebras.

We develop vertex and factorisation algebra analogues of the theory of quasitriangular bialgebras. Analogously to the classical theory, we prove their categories of representations are controlled by spectral R-matrices. In the vertex…

We discuss field theories appearing as a result of applying field transformations with derivatives (differential field transformations, DFT) to a known theory. We begin with some simple examples of DFTs to see the basic properties of the…

We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…

We consider Fourier transforms of densities supported on curves in R^d. We obtain sharp lower and close to sharp upper bounds for the L^q decay rates.

We show that physics-based simulations can be seamlessly integrated with NeRF to generate high-quality elastodynamics of real-world objects. Unlike existing methods, we discretize nonlinear hyperelasticity in a meshless way, obviating the…

We construct generalised diffeomorphisms for E$_9$ exceptional field theory. The transformations, which like in the E$_8$ case contain constrained local transformations, close when acting on fields. This is the first example of a…

Several classes of *-algebras associated to the action of an affine transformation are considered, and an investigation of the interplay between the different classes of algebras is initiated. Connections are established that relate…

The Baxterization process for the dynamical Yang-Baxter equation is studied. We introduce the local dynamical Hecke ,Temperley-Lieb and Birman-Murakami-Wenzl operators, then by inserting spectral parameters, from each representation of…

The explicit construction of direct and inverse Fourier's vector transform with discontinuous coefficients is presented. The technique of applying Fourier's vector transform with discontinuous coefficients for solving problems of…

We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X_1, ..., X_n ~ P \circ f, where P is a known measure. We focus on the two dimensional case where P and f are defined on R^2.…

Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical…

Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their…

We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.

We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…

Motivated in part by models arising from mathematical descriptions of Bose-Einstein condensation, we consider total variation minimization problems in which the total variation is weighted by a function that may degenerate near the domain…

In this paper, we investigate the behavior of the Fourier transform on finite dimensional 2-step Lie groups and develop a general theory akin to that of the whole space or the torus. We provide a familiar framework in which computations are…