Quantum toroidal gl(1) and Bethe ansatz

Abstract

We establish the method of Bethe ansatz for the XXZ type model obtained from the R-matrix associated to quantum toroidal gl(1). We do that by using shuffle realizations of the modules and by showing that the Hamiltonian of the model is obtained from a simple multiplication operator by taking an appropriate quotient. We expect this approach to be applicable to a wide variety of models.

Latex, 25 pages

References in corpus (4)

• Supersymmetric vacua and Bethe ansatz
• Kernel function and quantum algebras
• The Integrals of Motion for the Deformed Virasoro Algebra
• Commutative Families of the Elliptic Macdonald Operator

Cited by in corpus (18)

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• Anomaly in RTT relation for DIM algebra and network matrix models
• Decomposing Nekrasov Decomposition
• Integrals of motion from quantum toroidal algebras
• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• Instanton R-matrix and W-symmetry
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Gauge/Bethe correspondence from quiver BPS algebras
• Mixed network calculus
• Kerov functions revisited
• The $({\mathfrak{gl}}_m,{\mathfrak{gl}}_n$) duality in the quantum toroidal setting
• Shuffle approach towards quantum affine and toroidal algebras
• Kac determinant and singular vector of the level N representation of Ding-Iohara-Miki algebra
• Quantum deformation of Feigin-Semikhatov's W-algebras and 5d AGT correspondence with a simple surface operator
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture