Bases of Bethe Vectors and Difference Equations with Regular Singular Points

Abstract

We prove that Bethe vectors generically form a base in a tensor product of irreducible heighest weight $g{l}_2$-modules or $U_q(g{l}_2)$-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.

20 pages, (amstex.tex (ver. 2.1) is required)

References in corpus (2)

• Quantum Inverse Scattering Method. Selected Topics
• Quasiclassical asymptotics of solutions to the KZ equations

Cited by in corpus (5)

• On zero-remainder conditions in the Bethe ansatz
• A Q-operator for the twisted XXX model
• Non-regular eigenstate of the XXX model as some limit of the Bethe state
• Completing Bethe's equations at roots of unity
• On the Q operator and the spectrum of the XXZ model at root of unity