Related papers: Remarks on q-Virasoro and qKdV
Reflection and braid equations for rank two $q$-tensors are derived from the covariance properties of quantum vectors by using the $R$-matrix formalism.
Particular solutions of the Benney equations are constructed. Their properties are discussed.
We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces…
In this paper we establish some estimates of the right hand side of a Hermite-Hadamard type inequality in which some quasi-convex functions are involved.
The derivation of nonlinear integrable evolution partial differential equations in higher dimensions has always been the holy grail in the field of integrability. The well-known modified KdV equation is a prototypical example of integrable…
We revisit the Virasoro constraints and explore the relation to the Hirota bilinear equations. We furthermore investigate and provide the solution to non-homogeneous Virasoro constraints, namely those coming from matrix models whose domain…
We consider a Lie algebra generalizing the Virasoro algebra to the case of two space variables. We study its coadjoint representation and calculate the corresponding Euler equations. In particular, we obtain a bi-Hamiltonian system that…
We survey the various constructions of forward self-similar solutions (and generalizations of self-similar solutions) to the Navier-Stokes equations. We also include and prove an extension of a recent result from [7].
I examine the arguments which have been given for quantum fluctuation-dissipation theorems. I distinguish between a weak form of the theorem, which is true under rather general conditions, and a strong form which requires a Langevin…
In this note we associate to each Frobenius algebra a vertex algebra, the simplest example being the Virasoro vertex algebra. This construction is analogous to the procedure which associates to a Lie algebra with an invariant bilinear form…
A relativistic Coulomb-like resummation factor in QCD is suggested, based on the solution of the quasipotential equation.
This note is designed to show some classes of differential-difference equations admitting Lax representation which generalize evolutionary equations known in the literature.
We study integrals of the form $\int_{\Omega}f\left( d\omega\right)$, where $1\leq k\leq n$, $f:\Lambda^{k}\rightarrow\mathbb{R}$ is continuous and $\omega$ is a $\left(k-1\right)$-form. We introduce the appropriate notions of convexity,…
In relativistic potential models of quarkonia based on a Dirac-type of equation with a local potential there is a sharp distinction between a linear potential V which is vector-like and one which is scalar-like: There are normalizable…
In this note, we use recent advances concerning the K-stability of $\mathbb{Q}$-Fano varieties to provide settings for which Vojta's conjecture holds.
Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with…
The q-Painleve equation, satisfied by the Fourier transform of the q-Virasoro conformal blocks at c=1, is interpreted as a reformulation of the string equation and two other Virasoro constraints in the $5d$ Dotsenko-Fateev matrix model.
This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.
We show directly in the Lax operator approach how the Virasoro and W-constraints on the $\tau$-function arise in the $p$-reduced KP hierarchy or generalized KdV hierarchy. In partiacular, we consider the KdV and Boussinesq hierarchy to show…
We introduce integrable KdV type hierarchy associated naturally with arbitrary semi-simple Frobenius manifold. We present hierarchy in a Lax form and show that it admits bihamiltonian description.