Related papers: Fusion of SO(N) reflection matrices
There are two well-known ways of describing elements of the rotation group SO$(m)$. First, according to the Cartan-Dieudonn\'e theorem, every rotation matrix can be written as an even number of reflections. And second, they can also be…
By using of a special reduction way of density matrices, in this Letter we find the entanglement between two bunches of particles, its measure can be represented by the entanglement of formation.
The possibility that mirror matter with masses in the several hundred GeV- TeV range exists is explored. Mirror matter appears quite naturally in many unified models of particle interactions both in GUTs and in strings often in vector-like…
The classification of lepton mixing matrices from finite residual symmetries is reviewed, with emphasis on the role of vanishing sums of roots of unity for the solution of this problem.
Singular value decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions to finite complexes of real vector spaces. We provide two…
We implement our new Separation of Variables (SoV) approach for open quantum integrable models associated to higher rank representations of the reflection algebras. We construct the (SoV) basis for the fundamental representations of the…
Multi-loop calculations of the effective action for the matrix model are important for carrying out tests of the conjectured relationship of the matrix model to the low energy description of M-theory. In particular, comparison with…
Image decomposition is a crucial subject in the field of image processing. It can extract salient features from the source image. We propose a new image decomposition method based on convolutional neural network. This method can be applied…
We show that periodically doped, flat surfaces can act as reflective diffraction gratings for atomic and molecular matter waves. The diffraction element is realized by exploiting that charged dopants locally suppress quantum reflection from…
The study of the set-theoretic solutions of the reflection equation, also known as reflection maps, is closely related to that of the Yang-Baxter maps. In this work, we construct reflection maps on various geometrical objects, associated…
We propose a new hypermatrix singular value decomposition based upon the spectral decomposition of the symmetric products of transposes.
Fusion of positive energy representations is defined using Connes' tensor product for bimodules over a von Neumann algebra. Fusion is computed using the analytic theory of primary fields and explicit solutions of the Knizhnik-Zamolodchikov…
Many datasets in scientific and engineering applications are comprised of objects which have specific geometric structure. A common example is data which inhabits a representation of the group SO$(3)$ of 3D rotations: scalars, vectors,…
This is the first article in a series of two dealing with a matrix approach for aberration quantification and correction in ultrasound imaging. Advanced synthetic beamforming relies on a double focusing operation at transmission and…
Representations of $\text{SO}(4,2)$ are constructed using $4\times4$ and $2\times2$ matrices with elements in $\mathbb{H}'\otimes\mathbb{C}$, and the known isomorphism between the conformal group and $\text{SO}(4,2)$ is written explicitly…
We simulate the collision of atomic clusters with a weakly attractive surface using molecular dynamics in a regime between soft-landing and fragmentation, where the cluster undergoes large deformation but remains intact. As a function of…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
Consider the symmetric group $S_n$ acting as a reflection group on the polynomial ring $k[x_1, \ldots, x_n]$, where $k$ is a field such that Char$(k)$ does not divide $n!$. We use Higher Specht polynomials to construct matrix factorizations…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…