On the Gaudin model associated to Lie algebras of classical types

2015/12/31 by Kang Lu, E. Mukhin, Alexander Varchenko +1
Mathematics · Physics and Astronomy · #Adjoint representation of a Lie algebra #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Killing form #Lie algebra #Lie conformal algebra #Lie group #Mathematical physics #Mathematics #Physics #Pure mathematics #Theoretical physics #math-ph #math.MP #math.QA

paper · pdf · doi:10.1063/1.4964389

published as J. Math. Phys. 57, 101703 (2016) · LaTeX, 26 pages

openalex publication_date 2016/10/01 · arxiv created 2016/10/20 · arxiv updated 2016/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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.

Citations

• Quasi-polynomials and the Bethe Ansatz
• Remarks on critical points of phase functions and norms of Bethe vectors
• Critical Points of the Product of Powers of Linear Functions and Families of Bases of Singular Vectors