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arXiv · 1811.11225

Solutions of $\mathfrak{gl}_{m|n}$ XXX Bethe ansatz equation and rational difference operators

Chenliang Huang·Kang Lu·Evgeny Mukhin
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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.

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Chenliang Huang, Kang Lu, Evgeny Mukhin. 2018-11-27. Solutions of $\mathfrak{gl}_{m|n}$ XXX Bethe ansatz equation and rational difference operators. https://doi.org/10.1088/1751-8121%2Fab1960

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