Solutions of ${\mathfrak{gl}}_{m|n}$ 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 $\mathrm{Y}({\mathfrak{gl}}_{m|n})$. To a solution we associate a rational difference operator $\mathcal{D}$ and a superspace of rational functions $W$. We show that the set of complete factorizations of $\mathcal{D}$ 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.

LaTeX, 27 pages