Related papers: Reflection $K$-matrices related to Temperley-Lieb …
We present a classification of diagonal, antidiagonal and mixed reflection matrices related to Yangian and super-Yangian R matrices associated to the infinite series so(m), sp(n) and osp(m|n). We formulate the analytical Bethe Ansatz…
Strictly positive logics recently attracted attention both in the description logic and in the provability logic communities for their combination of efficiency and sufficient expressivity. The language of Reflection Calculus RC consists of…
We rigorously establish some exact properties of reflection symmetric spin systems with antiferromagnetic crossing bonds: At least one ground state has total spin zero and a positive semidefinite coefficient matrix. The crossing bonds obey…
A study of harmonic maps into Lie groups as a generalisation of the study of other well-known integrable systems, particularly the Toda and self-dual Chern Simons theories.
The Douglas-Rachford reflection method is a general purpose algorithm useful for solving the feasibility problem of finding a point in the intersection of finitely many sets. In this chapter we demonstrate that applied to a specific…
We consider matrix orthogonal polynomials related to Jacobi type matrices of weights that can be defined in terms of a given matrix Pearson equation. Stating a Riemann-Hilbert problem we can derive first and second order differential…
We investigate the (linearized) Morse index of solutions to Hamiltonan systems, with a focus on convex Hamiltonians functions and sign-changing radial solutions. For strongly coupled systems, we describe the profile of the radial solutions…
A review of the replica symmetric solution of the classical and quantum, infinite-range, Sherrington-Kirkpatrick spin glass is presented.
A Potts model with a reflecting boundary is introduced and it is shown that its partition function can be expressed as a Markov trace on the Temperley-Lieb Algebra of Coxeter type B.
We consider generalizations of Dunkl's differential-difference operators associated with groups generated by reflections. The commutativity condition is equivalent to certain functional equations. These equations are solved in many cases.…
The Lusztig-Shoji algorithm is generalized to a complex reflection group $W$ and give us a version of the Springer correspondence of $W$. We show that the combinatorics of generalized Springer correspondences of dihedral groups of order…
For a given quasitriangular Hopf algebra $\Ha$ we study relations between the braided group $\tilde \Ha^*$ and Drinfeld's twist. We show that the braided bialgebra structure of $\tilde \Ha^*$ is naturally described by means of twisted…
We analysis the symmetries of the reflection equation for open $XYZ$ model and find their solutions $K^{\pm}$ case by case. In the general open boundary conditions, the Lax pair for open one-dimensional $XYZ$ spin-chain is given.
We have find the diagonal K matrix solutions of the reflection equations for a class of vertex models. These models have (n+1)(2n+1) vertices and are defined as two set of (n + 1) R matrices, solutions of the equations of Yang-Baxter…
In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical…
The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of…
To every irreducible finite crystallographic reflection group (i.e., an irreducible finite reflection group G acting faithfully on an abelian variety X), we attach a family of classical and quantum integrable systems on X (with meromorphic…
To establish a relation between two approaches to the construction of Riemann k-wave solutions of hydrodynamic-type systems, namely the symmetry reduction method and the generalized method of characteristics.
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…
Knizhnik-Zamolodchikov-Bernard equations for twisted conformal blocks on compact Riemann surfaces with marked points are written explicitly in a general projective structure in terms of correlation functions in the theory of twisted b-c…