Solutions of XXX Bethe ansatz equation and rational difference operators

Abstract

We study solutions of the Bethe ansatz equations of the non-homogeneous periodic XXX model associated to super Yangian . To a solution we associate a rational difference operator and a superspace of rational functions W. We show that the set of complete factorizations of is in canonical bijection with the variety of superflags in W and that each generic superflag defines a solution of the Bethe ansatz equation. We also give the analogous statements for the quasi-periodic supersymmetric spin chains.