Related papers: Difference equations for the higher rank XXZ model…
By imposing special compatible similarity constraints on a class of integrable partial $q$-difference equations of KdV-type we derive a hierarchy of second-degree ordinary $q$-difference equations. The lowest (non-trivial) member of this…
This work provides a comparison principle for viscosity solutions to boundary value problems on (partially) bounded, cylindrical spaces. The comparison principle is based on a test function framework, that allows for the simultaneous…
We give an integral representation for solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations, in the case of sl(2). The result is based on a geometric construction of highest weight representations of the…
We find some exact solutions of the Knizhnik-Zamolodchikov equation for the four point correlation functions that occur in the SL(2,R) WZNW model. They exhibit logarithmic behaviour in both the Kac-Moody and Virasoro parts. We discuss their…
We propose an (essentially combinatorial) approach to the correlation functions of the domain wall six vertex model. We reproduce the boundary 1-point function determinant expression of Bogoliubov, Pronko and Zvonarev, then use that as a…
We study the quantum Knizhnik-Zamolodchikov equation of level $0$ associated with the spin $1/2$ representation of $U_q \bigl(\widehat{\frak s \frak l _{2}}\bigr)$. We find an integral formula for solutions in the case of an arbitrary total…
The spectral problem for the q-Knizhnik-Zamolodchikov equations for $U_{q}(\widehat{sl_2}) (0<q<1)$ at arbitrary level $k$ is considered. The case of two-point functions in the fundamental representation is studied in detail.The scattering…
We show how equivariant volumes of tensor product quiver varieties of type A are given by matrix elements of vertex operators of centrally extended doubles of Yangians, and how they satisfy in some cases the rational, level 1, quantum…
The trigonometric quantized Knizhnik-Zamolodchikov equation (qKZ equation) associated with the quantum group $U_q(sl_2)$ is a system of linear difference equations with values in a tensor product of $U_q(sl_2)$ Verma modules. We solve the…
We introduce certain correlation functions (graded $q$--traces) associated to vertex operator algebras and superalgebras which we refer to as $n$--point functions. These naturally arise in the studies of representations of Lie algebras of…
This article develops a duality principle applicable to a large class of variational problems. Firstly, we apply the results to a Ginzburg-Landau type model. In a second step, we develop another duality principle and related primal dual…
Let $X$ be a manifold with boundary, and let $L$ be a 0-elliptic operator on X which is semi-Fredholm essentially surjective with infinite-dimensional kernel. Examples include Hodge Laplacians and Dirac operators on conformally compact…
In the spirit of the quantum Hamiltonian reduction we establish a relation between the chiral $n$-point functions, as well as the equations governing them, of the $A_1^{(1)}$ WZNW conformal theory and the corresponding Virasoro minimal…
Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution…
In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This…
Boundary effect is a widespread idea in many-body theories. However, it is more of a conceptual notion than a rigorously defined physical quantity. One can quantify the boundary effect by comparing two ground states of the same physical…
We extend the concept of conjugate vertex operators, first introduced by Dotsenko in the case of the bosonization of the $su(2)$ conformal field theory, to the bosonization of the dynamical vertex operators (type II in the classification of…
A gradient dependent formula is derived for the spinless one-particle density-matrix operator z from the differential virial theorem. A gradient dependent formula is also derived for a spinless one-particle density-matrix operator that can…
In this paper, a new type of comparison theorem is presented for some initial-boundary value problems of second order nonlinear parabolic systems with nonlinear boundary conditions. This comparison theorem has an advantage over the…
We introduce a new fixed point theorem of Krasnoselskii type for discontinuous operators. As an application we use it to study the existence of positive solutions of a second-order differential problem with separated boundary conditions and…