A. Varchenko

activity

19942026

most citedGeometry of q-Hypergeometric Functions as a Bridge between Yangians and Quantum Affine Algebras

91 citations · 160 across the 14 of their papers we have counts for

collaborators

15 papers

math-ph2026

Eigenvectors and Eigenvalues of $p$ -Curvature Operators for KZ--type Differential Connections

Vitaly Tarasov, Alexander Varchenko

A KZ-type connection in characteristic $p$ has $p$ -curvature operators. These operators are commuting endomorphisms of the connection. We present a Bethe-ansatz-type construction o…

math.NT2026

Eigenvectors of $p$ -Curvature for Geometric Difference Equations

Vitaly Tarasov, Alexander Varchenko

A qKZ-type additive discrete flat connection in characteristic $p$ has $p$ -curvature operators. They are commuting automorphisms of the connection. We present a Bethe-ansatz-type c…

math-ph2026

Monodromy Eigenvectors for Difference Equations with Root-of-Unity Step

Vitaly Tarasov, Alexander Varchenko

A qKZ-type discrete flat connection with multiplicative step $p$ has monodromy operators when $p$ is a root of unity. The monodromy operators are commuting endomorphisms of the con…

math.NT2025

$p$ -curvature operators and Satake-type phenomenon for $sl_{2}$ KZ equations with $κ = \pm 2$

Prakash Belkale, Evgeny Mukhin, Alexander Varchenko

The $sl_{2}$ KZ differential equations with values in the tensor power of the fundamental representation with parameter $κ = \pm 2$ are considered. A Satake-type correspondence…

math-ph2025

Finding All Solutions of qKZ Equations in Characteristic $p$

Evgeny Mukhin, Alexander Varchenko

In [J. Lond. Math. Soc. 109 (2024), e12884, 22 pages, arXiv:2208.09721], the difference qKZ equations were considered modulo a prime number $p$ and a family of polynomial solutions…

math-ph2024

Finding all solutions to the KZ equations in characteristic $p$

Alexander Varchenko, Vadim Vologodsky

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…

Eigenvectors and Eigenvalues of p-Curvature Operators for KZ--type Differential Connections

Eigenvectors of p-Curvature for Geometric Difference Equations

Monodromy Eigenvectors for Difference Equations with Root-of-Unity Step

p-curvature operators and Satake-type phenomenon for sl2​ KZ equations with κ=±2

Finding All Solutions of qKZ Equations in Characteristic p

Finding all solutions to the KZ equations in characteristic p

Eigenvectors and Eigenvalues of $p$ -Curvature Operators for KZ--type Differential Connections

Eigenvectors of $p$ -Curvature for Geometric Difference Equations

$p$ -curvature operators and Satake-type phenomenon for $sl_{2}$ KZ equations with $κ = \pm 2$

Finding All Solutions of qKZ Equations in Characteristic $p$

Finding all solutions to the KZ equations in characteristic $p$