E. Mukhin

发表

A differential ideal of symmetric polynomials spanned by Jack polynomials at rβ = -(r=1)/(k+1)

Boris Feigin, Michio Jimbo, Tetsuji Miwa, 2001 .

On the Gaudin model of type G2

E. Mukhin, Kang Lu, 2017, Communications in Contemporary Mathematics.

Gaudin models for (m|n)

E. Mukhin, C. Young, B. Vicedo, 2014, 1404.3526.

On the number of populations of critical points of master functions

A. Varchenko, E. Mukhin, 2013, 1306.4429.

KZ Characteristic Variety as the Zero Set of Classical Calogero{Moser Hamiltonians

A. Varchenko, V. Tarasov, E. Mukhin, 2012, 1201.3990.

Three sides of the geometric Langlands correspondence for gl_N Gaudin model and Bethe vector averaging maps

A. Varchenko, V. Tarasov, E. Mukhin, 2009, 0907.3266.

ON SEPARATION OF VARIABLES AND COMPLETENESS OF THE BETHE ANSATZ FOR QUANTUM N GAUDIN MODEL

A. Varchenko, V. Tarasov, E. Mukhin, 2007, Glasgow Mathematical Journal.

Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel ?

A. Varchenko, V. Tarasov, E. Mukhin, 2007, math/0703893.

On the new form of Bethe ansatz equations and separation of variables in the $sl_3$ Gaudin model

A. Varchenko, V. Tarasov, E. Mukhin, 2006 .

Bethe eigenvectors of higher transfer matrices

Alexander Varchenko, Evgeny Mukhin, A. Varchenko, 2006 .

Higher Lame Equations and Critical Points of Master Functions

E. Mukhin, A. Varchenko, A. Varchenko, 2006 .

Norm of a Bethe vector and the Hessian of the master function

Alexander Varchenko, Evgeny Mukhin, A. Varchenko, 2005, Compositio Mathematica.

The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz

E. Mukhin, A. Varchenko, A. Varchenko, 2005 .

Discrete Miura Opers and Solutions of the Bethe Ansatz Equations

A. Varchenko, E. Mukhin, 2004, math/0401137.

Miura opers and critical points of master functions

A. Varchenko, E. Mukhin, 2003, math/0312406.

Critical points of master functions and flag varieties

E. Mukhin, A. Varchenko, A. Varchenko, 2002, math/0209017.

Remarks on critical points of phase functions and norms of Bethe vectors

A. Varchenko, E. Mukhin, 1998, math/9810087.

On algebraic equations satisfied by hypergeometric solutions of the qKZ equation

A. Varchenko, E. Mukhin, 1997, q-alg/9710040.

Braid actions on quantum toroidal superalgebras

E. Mukhin, L. Bezerra, 2019, 1912.08729.

Bosonic Formulas for Sl 2 Coinvariants

M. Jimbo, T. Miwa, E. Mukhin, 2022 .

Symmetric polynomials vanishing on the shifted diagonals and Macdonald polynomials

M. Jimbo, T. Miwa, B. Feigin, 2002, math/0209042.

Remarks on critical points of phase functions and norms of Bethe vectors

A. Varchenko, E. Mukhin, 1998, math/9810087.

The Hopf algebra $Rep U_q \hat{gl}_\infty$

E. Mukhin, E. Frenkel, 2001, math/0103126.

The q-Characters at Roots of Unity

E. Mukhin, E. Frenkel, 2001, math/0101018.

Combinatorics of q-Characters of Finite-Dimensional Representations of Quantum Affine Algebras

E. Mukhin, E. Frenkel, 1999, math/9911112.

The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz

A. Varchenko, V. Tarasov, E. Mukhin, 2005, math/0512299.

Sets of rigged paths with Virasoro characters

M. Jimbo, T. Miwa, Y. Takeyama, 2005, math/0506150.

Higher Lame Equations and Critical Points of Master Functions

A. Varchenko, V. Tarasov, E. Mukhin, 2006, math/0601703.

The Quantized Knizhnik-Zamolodchikov Equation in Tensor Products of Irreducible sl(2)-Modules

A. Varchenko, E. Mukhin, 1997, q-alg/9709026.

Combinatorics of the $ \widehat{\mathfrak{sl}}_2 $ spaces of coinvariants: loop Heisenberg modules and recursion

T. Miwa, R. Kedem, B. Feigin, 2002 .

Combinatorics of the $\hat{sl_2}$ spaces of coinvariants II

T. Miwa, R. Kedem, B. Feigin, 1999, math/0009198.

Bosonic formulas for $\hat{sl_2}$ coinvariants

M. Jimbo, T. Miwa, E. Mukhin, 2001, math/0107053.

Particle Content of the (k, 3)-configurations

M. Jimbo, T. Miwa, Y. Takeyama, 2002, math/0212348.

The hopf algebra rep $$U_q \widehat{\mathfrak{g}\mathfrak{l}}_\infty $$

E. Mukhin, E. Frenkel, 2002 .

Solutions of $ \newcommand{\g}{\mathfrak{g}} \newcommand{\n}{\mathfrak{n}} \newcommand{\gl}{\mathfrak{gl}} \gl_{m|n}$ XXX Bethe ansatz equation and rational difference operators

E. Mukhin, Kang Lu, CHE-HUNG Huang, 2019 .

Solutions of glm|n XXX Bethe ansatz equation and rational difference operators

E. Mukhin, Kang Lu, CHE-HUNG Huang, 2018, 1811.11225.

Extended T -System of Type G2 ?

E. Mukhin, Jian-Rong Li, 2012, 1208.4821.

Extended T-systems

E. Mukhin, C. Young, E. Mukhin, 2011, 1104.3094.

Gaudin Hamiltonians generate the Bethe algebra of a tensor power of vector representation of gl_N

A. Varchenko, V. Tarasov, E. Mukhin, 2009, 0904.2131.

Bethe Ansatz Equations for Orthosymplectic Lie Superalgebras and Self-dual Superspaces

Kang Lu, Evgeny Mukhin, E. Mukhin, 2021, Annales de l'Institute Henri Poincare. Physique theorique.

Bethe Algebra of Homogeneous XXX Heisenberg Model has Simple Spectrum

A. Varchenko, V. Tarasov, E. Mukhin, 2007, 0706.0688.

Spaces of quasi-exponentials and representations of the Yangian Y(gl_N)

A. Varchenko, V. Tarasov, E. Mukhin, 2013, 1303.1578.

Multiple orthogonal polynomials and a counterexample to the Gaudin Bethe Ansatz Conjecture

A. Varchenko, E. Mukhin, E. Mukhin, 2005, math/0501144.

Norm of a Bethe vector and the Hessian of the master function

A. Varchenko, E. Mukhin, 2004, Compositio Mathematica.

Jacobi–Trudi Identity and Drinfeld Functor for Super Yangian

E. Mukhin, Kang Lu, 2020, 2007.15573.

The gl_2 Bethe algebra associated with a nilpotent element

A. Varchenko, V. Tarasov, E. Mukhin, 2008, 0810.2257.

Spaces of quasi-exponentials and representations of

A. Varchenko, V. Tarasov, E. Mukhin, 2008, 0801.3120.

Schubert calculus and representations of the general linear group

E. Mukhin, A. Varchenko, A. Varchenko, 2007, 0711.4079.

Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel ?

A. Varchenko, V. Tarasov, E. Mukhin, 2007, math/0703893.

On the Supersymmetric XXX Spin Chains Associated to $$\mathfrak {gl}_{1|1}$$

Kang Lu, Evgeny Mukhin, E. Mukhin, 2019, Communications in Mathematical Physics.

Reality Property of Discrete Wronski Map with Imaginary Step

A. Varchenko, V. Tarasov, E. Mukhin, 2011, 1102.5368.

On reality property of Wronski maps

Alexander Varchenko, Evgeny Mukhin, A. Varchenko, 2007, 0710.5856.

Quasi-polynomials and the Bethe Ansatz

A. Varchenko, E. Mukhin, 2006, math/0604048.

Solutions to the XXX type Bethe ansatz equations and flag varieties

A. Varchenko, E. Mukhin, 2002, math/0211321.

Affinization of category O for quantum groups

E. Mukhin, C. Young, 2012, 1204.2769.

Path description of type B q-characters

E. Mukhin, C. Young, E. Mukhin, 2011, 1103.5873.

Affinization of category O for quantum groups

E. Mukhin, C. Young, E. Mukhin, 2012, 1204.2769.

Bethe subalgebras of the group algebra of the symmetric group

V. Tarasov, E. Mukhin, A. Varchenko, 2010 .

Quantum Toroidal Algebra Associated with 𝖌 𝖑 m | n

E. Mukhin, L. Bezerra, 2020 .

Quantum toroidal algebra associated with $\mathfrak{gl}_{m|n}$

E. Mukhin, L. Bezerra, 2019, 1904.07297.

Towards trigonometric deformation of sl^2 coset VOA

M. Jimbo, B. Feigin, E. Mukhin, 2018, Journal of Mathematical Physics.

Integrals of motion from quantum toroidal algebras

M. Jimbo, B. Feigin, E. Mukhin, 2017, 1705.07984.

Evaluation modules for quantum toroidal ${\mathfrak{gl}}_n$ algebras

M. Jimbo, B. Feigin, E. Mukhin, 2017, 1709.01592.

The solutions of $${\mathfrak {g}}{\mathfrak {l}}_{M|N}$$ Bethe ansatz equation and rational pseudodifferential operators

E. Mukhin, C. Young, B. Vicedo, 2019, Selecta Mathematica.

The solutions of glM|N Bethe ansatz equation and rational pseudodifferential operators

E. Mukhin, C. Young, B. Vicedo, 2019 .

Self-dual Grassmannian, Wronski map, and representations of $\mathfrak{gl}_N$, ${\mathfrak{sp}}_{2r}$, ${\mathfrak{so}}_{2r+1}$

A. Varchenko, E. Mukhin, Kang Lu, 2017, 1705.02048.

Bispectral and (glN, glM) dualities, discrete versus differential

A. Varchenko, V. Tarasov, E. Mukhin, 2008 .

Self-self-dual spaces of polynomials

E. Mukhin, L. Borisov, 2003, math/0308128.

Deformations of $$\mathcal {W}$$ algebras via quantum toroidal algebras

M. Jimbo, B. Feigin, E. Mukhin, 2020, 2003.04234.

Populations of solutions of the XXX Bethe equations associated to Kac-Moody algebras

A. Varchenko, E. Mukhin, 2002, math/0212092.

Quantum toroidal $\mathfrak{g}{{\mathfrak{l}}_{1}}$ and Bethe ansatz

M. Jimbo, T. Miwa, B. Feigin, 2015 .

Quantum toroidal gl 1 ?> and Bethe ansatz

M. Jimbo, T. Miwa, B. Feigin, 2015, 1502.07194.

SPACES OF QUASI-EXPONENTIALS AND REPRESENTATIONS OF THE YANGIAN $$ Y\left( {\mathfrak{g}{{\mathfrak{l}}_N}} \right) $$

A. Varchenko, V. Tarasov, E. Mukhin, 2014 .

Bethe algebra of the gl_{N+1} Gaudin model and algebra of functions on the critical set of the master function

V. Tarasov, E. Mukhin, A.Varchenko, 2009, 0910.4690.

Multiplicity of critical points of master functions and Schubert calculus

A. Varchenko, E. Mukhin, P. Belkale, 2005, math/0503132.

Bethe Algebra of Gaudin Model, Calogero–Moser Space, and Cherednik Algebra

A. Varchenko, V. Tarasov, E. Mukhin, 2009, 0906.5185.

The duality of glm|n and glk Gaudin models

E. Mukhin, CHE-HUNG Huang, 2020 .

Principal $\hat{sl}(3)$ subspaces and quantum Toda Hamiltonian

M. Jimbo, T. Miwa, B. Feigin, 2007, 0707.1635.

A Generalization of the Capelli Identity

A. Varchenko, V. Tarasov, E. Mukhin, 2006, math/0610799.

Quantum Toroidal Comodule Algebra of Type An−1 and Integrals of Motion

M. Jimbo, B. Feigin, E. Mukhin, 2021, Symmetry, Integrability and Geometry: Methods and Applications.

Quantum toroidal gl1-algebra: Plane partitions

M. Jimbo, B. Feigin, E. Mukhin, 2012 .

Combinatorics of vertex operators and deformed W-algebra of type D(2,1;α)

M. Jimbo, E. Mukhin, B. Feigin, 2021, Advances in Mathematics.

The $${(\mathfrak{gl}_{m},\mathfrak{gl}_{n})}$$(glm,gln) Duality in the Quantum Toroidal Setting

M. Jimbo, B. Feigin, E. Mukhin, 2018, Communications in Mathematical Physics.

Branching rules for quantum toroidal gl(n)

M. Jimbo, T. Miwa, B. Feigin, 2013, 1309.2147.

Fermionic Formulas for Eigenfunctions of the Difference Toda Hamiltonian

M. Jimbo, B. Feigin, E. Mukhin, 2008, 0812.2306.

A Monomial Basis for the Virasoro Minimal Series M(p,p′) : The Case 1

M. Jimbo, T. Miwa, Y. Takeyama, 2004, math/0405468.

Fermionic Formulas for (k , 3)-admissible Configurations

M. Jimbo, T. Miwa, Y. Takeyama, 2002, math/0212347.

Principal $\widehat{\mathfrak{sl}_3}$ subspaces and quantum Toda Hamiltonian

M. Jimbo, T. Miwa, B. Feigin, 2009 .

Representations of quantum affine algebras of type $B_N$

E. Mukhin, Matheus Brito, 2014, 1411.0562.

Form Factors and Action of on ∞-Cycles

Y. Takeyama, E. Mukhin, M. Jimbo, 2004 .

Form factors and action of U_{\sqrt{-1}}(sl_2~) on infinite-cycles

M. Jimbo, T. Miwa, Y. Takeyama, 2003, math/0305323.