Related papers: Fusion of SO(N) reflection matrices
In this paper, the canonical polyadic (CP) decomposition of tensors that corresponds to matrix multiplications is studied. Finding the rank of these tensors and computing the decompositions is a fundamental problem of algebraic complexity…
Let $W$ be a finite Coxeter group. We classify the reflection subgroups of $W$ up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup $R$ of $W$ the conjugacy class of its Coxeter…
The problem of the reflectance of a photon by a metallic mirror whose position is treated quantum mechanically is considered. The interaction between the metallic surface and the light is treated classically. It is shown that the…
Given a reflection group $G$ acting on a complex vector space $V$, a reflection map is the composition of an embedding $X \hookrightarrow V$ with the orbit map $V\to\mathbb C^p$ that maps a $G$-orbit to a point. Reflection maps can be very…
Transfer matrix method is a well-known and extensively used tool to compute the reflection and transmission coefficients of electromagnetic waves when interacting with a system of layers parallel to each other. We present here a modified…
A grand unified model based on SO(10) and supersymmetry is presented to account for the masses and mixing of the neutrinos observed in experiments.
Higgs multiplet in the vector-spinor representations of SO(10), i.e., the $144+\bar{144}$ multiplet can break the SO(10) gauge symmetry spontaneously in one step down to the Standard Model gauge group symmetry $SU(3)_C\times SU(2)_L\times…
Let $R$ be a Hecke solution to the Yang-Baxter equation and $K$ be a reflection equation matrix with coefficients in an associative algebra $\A$. Let $R(x)$ be the baxterization of $R$ and suppose that $K$ satisfies a polynomial equation…
Using the general approach of Lax for multiple scattering of waves a 2x2 covariant expression for the reflectivity of polarized slow neutrons of a magnetic layer structure of arbitrary complexity is given including polarization effects of…
We take matrix decompositions that are usually applied to matrices over the real numbers or complex numbers, and extend them to matrices over an algebra called the double numbers. In doing so, we unify some matrix decompositions: For…
We address the reflection of vector solitons, comprising several components that exhibit multiple field oscillations, at the interface between two nonlinear media. We reveal that reflection causes fission of the input signal into sets of…
In the conventional formulation of N=1 supersymmetry, a vector multiplet is supposed to be in the adjoint representation of a given gauge group. We present a new formulation with a vector multiplet in the non-adjoint representation of SO(N)…
We compute the correlation functions mixing the powers of two non-commuting random matrices within the same trace. The angular part of the integration was partially known in the literature: we pursue the calculation and carry out the…
A general fusion method to find solutions to the reflection equation in higher spin representations starting from the fundamental one is shown. The method is illustrated by applying it to obtaining the $K$ diagonal boundary matrices in an…
This note summarizes the steps to computing the best-fitting affine reflection that aligns two sets of corresponding points.
Let $X$ be a compact Riemann surface. A quadratic pair on $X$ consists of a holomorphic vector bundle with a quadratic form which takes values in fixed line bundle. We show that the moduli spaces of quadratic pairs of rank 2 are connected…
The scattering matrix, which quantifies the optical reflection and transmission of a photonic structure, is pivotal for understanding the performance of the structure. In many photonic design tasks, it is also desired to know how the…
We have found a (dense) basis for the N-representable, two-electron densities, in which all N-representable two-electron densities can be expanded, using positive coefficients. The inverse problem of finding a representative wavefunction,…
We initiate the combinatorial study of factorization systems on finite lattices, paying special attention to the role that reflective and coreflective factorization systems play in partitioning the poset of factorization systems on a fixed…
We consider one-plaquette unitary matrix model at finite $N$ using exact expression of the partition function for both SU($N$) and U($N$) groups.