Higher order Hamiltonians for the trigonometric Gaudin model

Abstract

We consider the trigonometric classical $r$-matrix for ${\mathfrak{gl}}_N$ and the associated quantum Gaudin model. We produce higher Hamiltonians in an explicit form by applying the limit $q\to 1$ to elements of the Bethe subalgebra for the $XXZ$ model.

arXiv comment14 pages

References in corpus (7)

• Gaudin Model, Bethe Ansatz and Critical Level
• Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety
• Bethe eigenvectors of higher transfer matrices
• Manin matrices and Talalaev's formula
• Higher Sugawara operators for the quantum affine algebras of type A
• FRT presentation of the Onsager algebras
• Center of the quantum affine vertex algebra associated with trigonometric R-matrix

Cited by in corpus (1)

• Difference Operators and Duality for Trigonometric Gaudin and Dynamical Hamiltonians