Related papers: Reflection matrices for the $U_{q}[spo(2n|2m)]$ ve…
The factorization condition for the scattering amplitudes of an integrable model with a line of defect gives rise to a set of Reflection-Transmission equations. The solutions of these equations in the case of diagonal $S$-matrix in the bulk…
We consider the primitive quaternionic reflection groups of type P for H^2 that are obtained from Blichfeldt's collineation groups for C^4.These are seen to be intimately related to the maximal set of five quaternionic mutually unbiased…
Neutron and X-ray reflectometry are powerful techniques facilitating the study of the structure of interfacial materials. The analysis of these techniques is ill-posed in nature requiring the application of a model-dependent methods. This…
We find the complete set of invertible solutions of the untwisted and twisted reflection equations for the Bazhanov-Jimbo R-matrix of type ${\mathrm A}^{(1)}_{N-1}$. We also show that all invertible solutions can be obtained by an…
We determine the intertwiners of a family of Onsager coideal subalgebras of the quantum affine algebra $U_p(A^{(1)}_{n-1})$ in the fundamental representations and $U_p(B^{(1)}_{n}), U_p(D^{(1)}_{n}), U_p(D^{(2)}_{n+1})$ in the spin…
We detail the automatic construction of R matrices corresponding to (the tensor products of) the (0|\alpha) families of highest-weight representations of the quantum superalgebras U_q[gl(m|n)]. These representations are irreducible, contain…
By using a generalization of Sturm-Liouville problems in $q$-difference spaces, a class of symmetric $q$-orthogonal polynomials with four free parameters is introduced. The standard properties of these polynomials, such as a second order…
We explore different limits of exactly solvable vector and matrix fermionic quantum mechanical models with quartic interactions at finite temperature. The models preserve a $U(1)\times SU(N)\times SU(L)$ symmetry at the classical level and…
A modular form on an even lattice $M$ of signature $(l,2)$ is called reflective if it vanishes only on quadratic divisors orthogonal to roots of $M$. In this paper we show that every reflective modular form on a lattice of type $2U\oplus L$…
Here we introduce reflection positive doubles, a general framework for reflection positivity, covering a wide variety of systems in statistical physics and quantum field theory. These systems may be bosonic, fermionic, or parafermionic in…
The type-I simple Lie-superalgebras are $sl(m|n)$ and $osp(2|2n)$. We study the quantum deformations of their untwisted affine extensions $U_q(sl(m|n)^{(1)})$ and $U_q(osp(2|2n)^{(1)})$. We identify additional relations between the simple…
In this paper I construct lattice models with an underlying $U_q osp(2,2)$ superalgebra symmetry. I find new solutions to the graded Yang-Baxter equation. These {\it trigonometric} $R$-matrices depend on {\it three} continuous parameters,…
In this letter, we consider exact $\mu-\tau$ reflection symmetries for quarks and leptons. Fermion mass matrices are assumed to be four-zero textures for charged fermions $f = u,d,e$ and a symmetric matrix for neutrinos $\nu_{L}$. By a…
We discuss the integrable boundary conditions for the one-dimensional (1D) Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM). We use the fermionic R-matrix proposed by Olmedilla et al. to treat the twisted…
We formulate N-fold supersymmetry in quantum mechanical systems with reflection operators. As in the cases of other systems, they possess the two significant characters of N-fold supersymmetry, namely, almost isospectrality and weak…
It has recently been shown that periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. The standard treatment gets these band gaps from an eigenvalue equation for the Bloch factor…
Masses of fermions in the SO(10) 16-plet are constructed using only the 10, 120 and 126 scalar multiplets. The mass matrices are restricted to be hermitian and the theory is constructed to have certain assumed quark masses, charged lepton…
We classify all the symmetric integer bilinear forms of signature (2,1) whose isometry groups are generated up to finite index by reflections. There are 8595 of them up to scale, whose 374 distinct Weyl groups fall into 39 commensurability…
This note presents explicit matrix expressions of a class of recently-discovered non-diagonal K-matrices for the trigonometric $A^{(1)}_{n-1}$ vertex model. From these explicit expressions, it is easily seen that in addition to a {\it…
A strongly correlated electron system associated with the quantum superalgebra ${U}_q[{osp}(2|2)]$ is studied in the framework of the quantum inverse scattering method. By solving the graded reflection equation, two classes of…