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.

arXiv commentLaTeX, 27 pages

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Cited by in corpus (11)

• Rational $Q$-systems, Higgsing and Mirror Symmetry
• Jacobi-Trudi identity and Drinfeld functor for super Yangian
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• A note on odd reflections of super Yangian and Bethe ansatz
• Bethe ansatz equations for orthosymplectic Lie superalgebras and self-dual superspaces
• On the supersymmetric XXX spin chains associated to ${\mathfrak{gl}}_{1|1}$
• Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra
• Completeness of Bethe ansatz for Gaudin models associated with gl(1|1)
• On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
• Superopers revisited