Extensions of a commuting pair of quantum toroidal \mathfrakgl₁

2025/12/25 by B. Feigin, Feigin, B., M. Jimbo +3
Mathematics · Computer Science · #Algebraic structures and combinatorial models #Quantum Computing Algorithms and Architecture #Advanced Combinatorial Mathematics

paper · doi:10.48550/arxiv.2512.21750

Abstract

We introduce a family of algebras A_M,N, M,N∈ℤ, as an extension of a pair of commuting quantum toroidal \mathfrakgl₁ subalgebras E₁,\checkE₁, wherein the parameters are tuned in a specific way according to M,N. In the case M=± 1, algebra A_±1,N is a shifted quantum toroidal \mathfrakgl₂ algebra introduced in [FJM2]. Conjecturally there is a coproduct homomorphism A_M,N1+N2\toA_M,N1\otimesA_M,N2 to a completed tensor product, whose restriction to the subalgebras E₁,\checkE₁ coincides with the standard Drinfeld coproduct. We give examples of A_M,N modules constructed on certain direct sums of tensor products of Fock modules of E₁⊗\checkE₁.

Citations

• Extensions of deformed W-algebras via qq-characters
• Toward AGT for parabolic sheaves
• Vertex Algebras for S-duality

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