Related papers: Differential equations compatible with boundary ra…
We express the defining relations of the $q$-deformed Minkowski space algebra as well as that of the corresponding derivatives and differentials in the form of reflection equations. This formulation encompasses the covariance properties…
Differential equations are derived for a continuous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry.
By applying suitable centrality condition to non-commutative non-isospectral lattice modified Gel'fand-Dikii type systems we obtain the corresponding non-autonomous equations. Then we derive non-commutative q-discrete Painleve VI equation…
The KZ equations are differential equations satisfied by the correlation functions (on the Riemann sphere) of two-dimensional conformal field theories associated with an affine Lie algebra at a fixed level. They form a system of complex…
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…
In this paper, we study the Wong-Zakai approximation of the solution to the stochastic differential equation on a domain $D$ in a Euclidean space with normal reflection at the boundary. We prove the $L^p$ convergence of the approximation in…
We introduce a universal framework for boundary transfer matrices, inspired by Sklyanin's two-row transfer matrix approach for quantum integrable systems with boundary conditions. The main examples arise from quantum symmetric pairs of…
We analyse divergent diagrams of \(k\)-fold map-germs on \((\mathbb{C}^n,0)\), for $k, n \geq 2$, associated with reflections, adapting to the complex setting the theory of folds associated with involutions on \((\mathbb{R}^n,0)\). In the…
We study steady Boltzmann equation in half-space, which arises in the Knudsen boundary layer problem, with diffusive reflection boundary conditions. Under certain admissible conditions and the source term decaying exponentially, we…
For finite dimensional CMV matrices the mixed inverse spectral problem of reconstruction the matrix by its submatrix and a part of its spectrum is considered. A general rational interpolation problem which arises in solving the mixed…
The differential equation proposed by Frits Zernike to obtain a basis of polynomial orthogonal solutions on the the unit disk to classify wavefront aberrations in circular pupils, is shown to have a set of new orthonormal solution bases,…
We prove that linear collisional kinetic equations in the whole space without confinement mechanism display a long-time self-similar behaviour. This drastically improves the recently known results (decay estimates) about the solutions in…
We present a new construction related to systems of polynomials which are consistent on a cube. The consistent polynomials underlie the integrability of discrete counterparts of integrable partial differential equations of Korteweg- de…
Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations,…
This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…
We consider the Knizhnik-Zamolodchikov (KZ) and dynamical equations, both differential and difference, in the context of the (gl_k,gl_n) duality. We show that the KZ and dynamical equations naturally exchange under the duality.
We consider a two-dimensional commutative algebra B over the field of complex numbers. The algebra B is associated with the biharmonic equation. For monogenic functions with values in B, we consider a Schwartz-type boundary value problem…
We prove that the equivariant derived category for a finite subgroup of GL(3,C) has a semi-orthogonal decomposition into the derived category of a certain partial resolution, called a maximal Q-factorial terminalization, of the…
We consider commutativity equations $F_i F_j =F_j F_i$ for a function $F(x^1, \dots, x^N),$ where $F_i$ is a matrix of the third order derivatives $F_{ikl}$. We show that under certain non-degeneracy conditions a solution $F$ satisfies the…
For the Lie algebra $gl_N$ we introduce a system of differential operators called the dynamical operators. We prove that the dynamical differential operators commute with the $gl_N$ rational quantized Knizhnik-Zamolodchikov difference…