Related papers: Differential equations compatible with boundary ra…

We construct a categorification of the modular data associated with every family of unipotent characters of the spetsial complex reflection group $G(d,1,n)$. The construction of the category follows the decomposition of the Fourier matrix…

The quantized Knizhnik-Zamolodchikov equations associated with the trigonometric R-matrix or the rational R-matrix of the A-type are considered. Jackson integral representations for solutions of these equations are described. Asymptotic…

In this paper we identify the cotangent to the derived stack of representations of a quiver $Q$ with the derived moduli stack of modules over the Ginzburg dg-algebra associated with $Q$. More generally, we extend this result to finite type…

In this paper we first study the penalization approximation of stochastic differential equations reflected in a domain which satisfies conditions (A) and (B) and prove that the sequence of solutions of the penalizing equations converges in…

We extend Halphen's theorem which characterizes the solutions of certain $n$th-order differential equations with rational coefficients and meromorphic fundamental systems to a first-order $n \times n$ system of differential equations. As an…

We study the degenerate linear Boltzmann equation inside a bounded domain with a generalized diffuse reflection at the boundary and variable temperature, including the Maxwell boundary conditions with the wall Maxwellian or heavy-tailed…

We prove radial symmetry of singular solutions to an overdetermined boundary value problem for a class of degenerate quasilinear elliptic equations.

We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems. We focuse on the logarithmic and non-resonant case, which describes the geometric situation. We show that quantum differential systems provide a…

Cherednik's type A quantum affine Knizhnik-Zamolodchikov (qKZ) equations form a consistent system of linear $q$-difference equations for $V_n$-valued meromorphic functions on a complex $n$-torus, with $V_n$ a module over the GL${}_n$-type…

We introduce the notion of $N$-reflection equation which provides a large generalization of the usual classical reflection equation describing integrable boundary conditions. The latter is recovered as a special example of the $N=2$ case.…

We present a quantum version of the construction of the KZ system of equations as a flat connection on the spaces of coinvariants of representations of tensor products of Kac-Moody algebras. We consider here representations of a tensor…

We investigate the possible regular solutions of the boundary Yang-Baxter equation for the fundamental $U_q[G_2]$ vertex model. We find four distinct classes of reflection matrices such that half of them are diagonal while the other half…

Let $W$ be an irreducible complex reflection group acting on its reflection representation $V$. We consider the doubly graded action of $W$ on the exterior algebra $\wedge (V \oplus V^*)$ as well as its quotient $DR_W := \wedge (V \oplus…

In this paper we prove a general approximation result for reflected stochastic differential equations in bounded domains satisfying conditions reorganized by Ren and Wu. Then we show that it includes Wong-Zakai approximation, mollifier…

Motivated by earlier works we employ appropriate realizations of the affine Hecke algebra and we recover previously known non-diagonal solutions of the reflection equation for the $U_{q}(\hat{gl_n})$ case. The corresponding $N$ site spin…

Using the Quantum Inverse Scattering Method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six vertex model with reflecting end.

A solution to the reflection equation associated to a coideal subalgebra of $U_q(A_{2n-1}^{(1)})$ of type AII in the symmetric tensor representations is presented. If parameters of the coideal subalgebra are suitably chosen, the $K$ matrix…

A class of backward doubly stochastic differential equations (BDSDEs in short) with continuous coefficients is studied. We give the comparison theorems, the existence of the maximal solution and the structure of solutions for BDSDEs with…

We introduce a class of induced representations of the degenerate double affine Hecke algebra of gl_N and analyze their structure mainly by means of intertwiners. We also construct them from modules of the affine Lie algebra using…

We describe a bilinear identity satisfied by certain multidimensional q-hypergeometric integrals. The identity can be considered as a deformation of the Riemann bilinear relation for the twisted de Rham (co)homologies. The identity also…