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Solutions of $\mathfrak{gl}_{m|n}$ XXX Bethe ansatz equation and rational difference operators (1811.11225v1)
Published 27 Nov 2018 in math.QA, math-ph, and math.MP
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.