M. Jimbo

activity

19942024

gl_{1}

algebra : plane partitions

99 citations · 400 across the 17 of their papers we have counts for

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14 papers · 1 filter

math.QA2024

Remarks on $q$ -difference opers arising from quantum toroidal algebras

B. Feigin, M. Jimbo, E. Mukhin

We propose a conjectural correspondence between the spectra of the Bethe algebra for the quantum toroidal $gl_{2}$ algebra on relaxed Verma modules, and $q$ -hypergeometric…

math.QA2024

Combinatorial bases in quantum toroidal $gl_{2}$ modules

Michio Jimbo, Evgeny Mukhin

We show that many tame modules of the quantum toroidal $gl_{2}$ algebra can be explicitly constructed in a purely combinatorial way using the theory of $q$ -characters. The…

math.QA2023

Commutative subalgebra of a shuffle algebra associated with quantum toroidal $gl_{m ∣ n}$

B. Feigin, M. Jimbo, E. Mukhin

We define and study the shuffle algebra $S h_{m ∣ n}$ of the quantum toroidal algebra $E_{m ∣ n}$ associated to Lie superalgebra $gl_{m ∣ n}$ . We show that $S h_{m ∣ n}$ …

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.QA2021

Quantum Toroidal Comodule Algebra of Type $A_{n - 1}$ and Integrals of Motion

Boris Feigin, Michio Jimbo, Evgeny Mukhin

We introduce an algebra $K_{n}$ which has a structure of a left comodule over the quantum toroidal algebra of type $A_{n - 1}$ . Algebra $K_{n}$ is a higher rank gener…

math.QA2020★ 4 cited

Deformations of $W$ algebras via quantum toroidal algebras

B. Feigin, M. Jimbo, E. Mukhin +1

The deformed $W$ algebras of type $A$ have a uniform description in terms of the quantum toroidal $gl_{1}$ algebra $E$ . We introduce a comodule…

math.QA2018★ 9 cited

Towards trigonometric deformation of $sl_{2}$ coset VOA

B. Feigin, M. Jimbo, E. Mukhin

We discuss the quantization of the $sl_{2}$ coset vertex operator algebra $W D (2, 1; α)$ using the bosonization technique. We show that after quantization…

math.QA2018★ 10 cited

The $(gl_{m}, gl_{n}$ ) duality in the quantum toroidal setting

B. Feigin, M. Jimbo, E. Mukhin

On a Fock space constructed from $mn$ free bosons and lattice $Z^{mn}$ , we give a level $n$ action of the quantum toroidal algebra $E_{m}$ associated to $\mathfra…

math.QA2016★ 22 cited