Quantum toroidal comodule algebra of type \(A_{n-1}\) and integrals of motion

DOI10.3842/SIGMA.2022.051zbMath1492.81062arXiv2112.14631OpenAlexW4284707433MaRDI QIDQ2162649

Evgenii E. Mukhin, Michio Jimbo, Boris L. Feigin

Publication date: 8 August 2022

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.14631

zbMATH Keywords

quantum toroidal algebrasintegrals of motioncomodule

Mathematics Subject Classification ID

Vertex operators; vertex operator algebras and related structures (17B69) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Applications of Lie algebras and superalgebras to integrable systems (17B80)

Related Items

Commutative subalgebra of a shuffle algebra associated with quantum toroidal \(\mathfrak{gl}_{m|n}\)

Cites Work

• Unnamed Item
• Branching rules for quantum toroidal \(\mathfrak{gl}_n\)
• Quantum symmetric Kac-Moody pairs
• The integrals of motion for the deformed \(W\)-algebra \(W_{q,t}(\widehat{gl_N})\). II: Proof of the commutation relations
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• The ${(\mathfrak{gl}_{m},\mathfrak{gl}_{n})}$ duality in the quantum toroidal setting
• Integrable structure of BCD conformal field theory and boundary Bethe ansatz for affine Yangian
• The \(R\)-matrix of the quantum toroidal algebra \(U_{q,t}(\overset{..}{gl}_1)\) in the Fock module
• Deformations of \(\mathcal{W}\) algebras via quantum toroidal algebras
• A Drinfeld type presentation of affine \(\imath\) quantum groups. I: Split ADE type
• Generalized Macdonald functions on Fock tensor spaces and duality formula for changing preferred direction
• Non-stationary Ruijsenaars functions for \(\kappa = t^{-1/N}\) and intertwining operators of Ding-Iohara-Miki algebra
• Finite type modules and Bethe ansatz for quantum toroidal \(\mathfrak{gl}_1\)
• Liouville reflection operator, affine Yangian and Bethe ansatz
• Integrals of motion from quantum toroidal algebras
• Boundary conditions for integrable quantum systems
• COIDEAL SUBALGEBRAS IN QUANTUM AFFINE ALGEBRAS
• Quasimap counts and Bethe eigenfunctions
• TOROIDAL q-OPERS
• Quantum toroidal algebras and their vertex representations