E. Mukhin

activity

20022026

most citedBethe eigenvectors of higher transfer matrices

52 citations · 153 across the 19 of their papers we have counts for

collaborators

19 papers

math.QA2026

Monodromy free Schrödinger operators and affine $sl_{2}$ master functions

Andrei Grigorev, Evgeny Mukhin

Given a non-zero polynomial $P (x)$ , we study Fuchsian differential operators of the form $L = \partial_{x}^{2} - u (x)$ such that for all $λ \in C$ the operator $L + λ P (x)$ is monodrom…

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.CV2024

Positivity and universal Plücker coordinates for spaces of quasi-exponentials

Steven N. Karp, Evgeny Mukhin, Vitaly Tarasov

A quasi-exponential is an entire function of the form $e^{c u} p (u)$ , where $p (u)$ is a polynomial and $c \in C$ . Let $V = \langle e^{h_1u}p_1(u), \dots, e^{h_Nu}p_N(u) \ran…

math.QA2022

Extensions of deformed $W$ -algebras via $q q$ -characters

B. Feigin, M. Jimbo, E. Mukhin

We use combinatorics of $q q$ -characters to study extensions of deformed $W$ -algebras. We describe additional currents and part of the relations in the cases of $gl (n ∣ m)$ …

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…

Monodromy free Schrödinger operators and affine sl2​ master functions

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

Finding All Solutions of qKZ Equations in Characteristic p