A. Varchenko

activity

19932023

most citedGeometry and classification of solutions of the Classical Dynamical Yang-Baxter Equation

167 citations · 1.9k across the 134 of their papers we have counts for

collaborators

152 papers

math-ph2023

Hypergeometric integrals, hook formulas and Whittaker vectors

G. Felder, A. Smirnov, V. Tarasov +1

We determine the coefficient of proportionality between two multidimensional hypergeometric integrals. One of them is a solution of the dynamical difference equations associated wi…

math-ph2023

Polynomial superpotential for Grassmannian $G r (k, n)$ from a limit of vertex function

Andrey Smirnov, Alexander Varchenko

In this note we discuss an integral representation for the vertex function of the cotangent bundle over the Grassmannian, $X = T^{*} G r (k, n)$ . This integral representation can be use…

math.AG2023

Polynomial Solutions Modulo $p^{s}$ of Differential KZ and Dynamical Equations

Pavel Etingof, Alexander Varchenko

We construct polynomial solutions modulo $p^{s}$ of the differential KZ and dynamical equations where $p$ is an odd prime number.

math-ph2023★ 2 cited

The p-adic approximations of vertex functions via 3D-mirror symmetry

Andrey Smirnov, Alexander Varchenko

Using the $3 D$ mirror symmetry we construct a system of polynomials $T_{s} (z)$ with integral coefficients which solve the quantum differential equitation of $X = T^{*} G r (k, n)$ modulo…

math-ph2022

Monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian

Vitaly Tarasov, Alexander Varchenko

We describe the monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian in terms of the equivariant K-theory algebra of the cotangent b…

math.QA2022★ 2 cited

Solutions of the $s l_{2}$ qKZ equations modulo an integer

Evgeny Mukhin, Alexander Varchenko

We study the qKZ difference equations with values in the $n$ -th tensor power of the vector $s l_{2}$ representation $V$ , variables $z_{1}, \dots, z_{n}$ and integer step $κ$ . For any intege…

Hypergeometric integrals, hook formulas and Whittaker vectors

Polynomial superpotential for Grassmannian Gr(k,n) from a limit of vertex function

Polynomial Solutions Modulo ps of Differential KZ and Dynamical Equations

The p-adic approximations of vertex functions via 3D-mirror symmetry

Monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian

Solutions of the sl2​ qKZ equations modulo an integer

Polynomial superpotential for Grassmannian $G r (k, n)$ from a limit of vertex function

Polynomial Solutions Modulo $p^{s}$ of Differential KZ and Dynamical Equations

Solutions of the $s l_{2}$ qKZ equations modulo an integer