Bases of Bethe Vectors and Difference Equations with Regular Singular Points

1995/04/20 by Vitaly Tarasov, Tarasov, Vitaly, Alexander Varchenko +1
Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.q-alg/9504011

openalex publication_date 1995/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that Bethe vectors generically form a base in a tensor product of irreducible heighest weight gl₂-modules or U_q(gl₂)-modules. We apply this result to difference equations with regular singular points. We show that if such an equation has local solutionss at each of its singular point, then generically it has a polynomial solution.

Related

• Bethe algebra and algebra of functions on the space of differential operators of order two with polynomial solutions
• SU(N) Matrix Difference Equations and a Nested Bethe Ansatz
• On Bethe vectors in the sl_N+1 Gaudin model
• Bethe Algebra of Homogeneous XXX Heisenberg Model Has Simple Spectrum
• The solutions of \mathfrakgl_M|N Bethe ansatz equation and rational pseudodifferential operators