Bases of Bethe Vectors and Difference Equations with Regular Singular Points
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We 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)
20 pages, (amstex.tex (ver. 2.1) is required)