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math.AG2005
The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz
E. Mukhin, V. Tarasov, A. Varchenko
We prove the B. and M. Shapiro conjecture that says that if the Wronskian of a set of polynomials has real roots only, then the complex span of this set of polynomials has a basis…
math.QA2005★ 11 cited
Multiple orthogonal polynomials and a counterexample to Gaudin Bethe Ansatz Conjecture
E. Mukhin, A. Varchenko
Jacobi polynomials are polynomials whose zeros form the unique solution of the Bethe Ansatz equation associated with two sl_2 irreducible modules. We study sequences of r polynomia…