The integrals of motion for the deformed \(W\)-algebra \(W_{q,t}(\widehat{gl_N})\). II: Proof of the commutation relations

DOI10.1007/s00220-008-0524-3zbMath1190.17013arXiv0709.2305OpenAlexW2014599944MaRDI QIDQ958166

Jun'ichi Shiraishi, Takeo Kojima

Publication date: 2 December 2008

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.2305

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Virasoro and related algebras (17B68) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (7)

Quantum toroidal comodule algebra of type \(A_{n-1}\) and integrals of motion ⋮ Integrals of motion from quantum toroidal algebras ⋮ The integrals of motion for the elliptic deformation of the Virasoro and algebra ⋮ Non-stationary Ruijsenaars functions for \(\kappa = t^{-1/N}\) and intertwining operators of Ding-Iohara-Miki algebra ⋮ The ${(\mathfrak{gl}_{m},\mathfrak{gl}_{n})}$ duality in the quantum toroidal setting ⋮ WAKIMOTO REALIZATION OF THE ELLIPTIC QUANTUM GROUP $U_{q,p}(\widehat{{\rm sl}_N})$ ⋮ Quadratic relations of the deformed W-superalgebra Wq,tA(M,N)

Cites Work

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• The elliptic algebra \(U_{q,p}(\widehat{\mathfrak{sl}}_N)\) and the Drinfeld realization of the elliptic quantum group \(\mathcal B_{q,\lambda}(\widehat{\mathfrak{sl}}_N)\).
• Kac-Moody groups and integrability of soliton equations
• Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz
• A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions
• Quantum affine algebras and deformations of the Virasoro and \({\mathcal W}\)-algebras
• Quantum \({\mathcal W}\)-algebras and elliptic algebras
• Quantum \({\mathcal W}_ N\) algebras and Macdonald polynomials
• Bosonization of vertex operators for the face model
• Integrable structure of \(W_3\) conformal field theory, quantum Boussinesq theory and boundary affine Toda theory

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