E. Mukhin

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math.QA2025

Extensions of a commuting pair of quantum toroidal $gl_{1}$

B. Feigin, M. Jimbo, E. Mukhin

We introduce a family of algebras $A_{M, N}$ , $M, N \in Z$ , as an extension of a pair of commuting quantum toroidal $gl_{1}$ subalgebras $\mathcal{E}_1,\che…

math.QA2025

Affinization of shifted quantum affine $gl_{2}$

B. Feigin, M. Jimbo, E. Mukhin

We give a realization $A_{0}$ of quantum toroidal algebra associated to $gl_{2}$ which can be viewed as an affinization of the Drinfeld new realization of quantum…

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 $S h_{m ∣ n}$ …

Extensions of a commuting pair of quantum toroidal gl1​

Affinization of shifted quantum affine gl2​

Commutative subalgebra of a shuffle algebra associated with quantum toroidal glm∣n​

Extensions of a commuting pair of quantum toroidal $gl_{1}$

Affinization of shifted quantum affine $gl_{2}$

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