Gaudin Hamiltonians generate the Bethe algebra of a tensor power of vector representation of gl_N

Abstract

We show that the Gaudin Hamiltonians H_1,...,H_n generate the Bethe algebra of the n-fold tensor power of the vector representation of gl_N. Surprisingly the formula for the generators of the Bethe algebra in terms of the Gaudin Hamiltonians does not depend on N. Moreover, this formula coincides with Wilson's formula for the stationary Baker-Akhiezer function on the adelic Grassmannian.

arXiv commentLatex, 11 pages

References in corpus (4)

• Off-Shell Bethe Ansatz Equation and N-point Correlators in the SU(2) WZNW Theory
• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
• Quantization of the Gaudin System
• Schubert calculus and representations of general linear group

Cited by in corpus (13)

• On Three Dimensional Quiver Gauge Theories and Integrability
• Classical tau-function for quantum spin chains
• Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
• Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra
• KZ Characteristic Variety as the Zero Set of Classical Calogero-Moser Hamiltonians
• Quantum Integrable Model of an Arrangement of Hyperplanes
• The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy
• Bethe subalgebras of the group algebra of the symmetric group
• Quantum-classical duality for Gaudin magnets with boundary
• Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)
• On the classical r-matrix structure of the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• Quadratic and cubic Gaudin Hamiltonians and super Knizhnik-Zamolodchikov equations for general linear Lie superalgebras
• Symmetric functions for the generating matrix of Yangian of gl_n(C)