On the Gaudin model associated to Lie algebras of classical types

Abstract

We derive explicit formulas for solutions of the Bethe Ansatz equations of the Gaudin model associated to the tensor product of one arbitrary finite-dimensional irreducible module and one vector representation for all simple Lie algebras of classical type. We use this result to show that the Bethe Ansatz is complete in any tensor product where all but one factor are vector representations and the evaluation parameters are generic. We also show that except for the type D, the joint spectrum of Gaudin Hamiltonians in such tensor products is simple.

arXiv commentLaTeX, 26 pages

References in corpus (8)

• Quasiclassical asymptotics of solutions to the KZ equations
• Bethe eigenvectors of higher transfer matrices
• Quasi-polynomials and the Bethe Ansatz
• Quantum Integrable Model of an Arrangement of Hyperplanes
• Gaudin models for gl(m|n)
• Critical Points of the Product of Powers of Linear Functions and Families of Bases of Singular Vectors
• Eigenvalues of Bethe vectors in the Gaudin model
• Remarks on critical points of phase functions and norms of Bethe vectors

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• Gaudin Hamiltonians on unitarizable modules over classical Lie (super)algebras
• On the Gaudin model of type G${}_2$
• Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus
• Yang-Yang functions, Monodromy and knot polynomials