Bethe ansatz equations for orthosymplectic Lie superalgebras and self-dual superspaces

Abstract

We study solutions of the Bethe ansatz equations associated to the orthosymplectic Lie superalgebras ${\mathfrak{osp}}_{2m+1|2n}$ and ${\mathfrak{osp}}_{2m|2n}$. Given a solution, we define a reproduction procedure and use it to construct a family of new solutions which we call a population. To each population we associate a symmetric rational pseudo-differential operator $\mathcal{R}$. Under some technical assumptions, we show that the superkernel $W$ of $\mathcal{R}$ is a self-dual superspace of rational functions, and the population is in a canonical bijection with the variety of isotropic full superflags in $W$ and with the set of symmetric complete factorizations of $\mathcal{R}$. In particular, our results apply to the case of even Lie algebras of type D${}_m$ corresponding to ${\mathfrak{osp}}_{2m|0}={\mathfrak{so}}_{2m}$.

34 pages

References in corpus (5)

• Bethe eigenvectors of higher transfer matrices
• Quasi-polynomials and the Bethe Ansatz
• Jacobi-Trudi identity and Drinfeld functor for super Yangian
• Gaudin models for gl(m|n)
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• Superopers revisited