2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153377We prove that Bethe vectors generically form a base in a tensor product of irreducible heighest weight $gl_2$-modules or $U_q(gl_2)$-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)Quantum Algebratext