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 \(\mathfrak {osp}_{2m|0}=\mathfrak {so}_{2m}\).

我们研究与正辛李超代数\(\mathfrak {osp}_{2m+1|2n}\)和\(\mathfrak {osp}_{2m|2n}\)相关的 Bethe ansatz 方程的解。给定一个解决方案，我们定义一个再生产过程并使用它来构建一个我们称之为种群的新解决方案族。对于每个种群，我们关联一个对称有理伪微分算子\(\mathcal R\)。在一些技术假设，我们表明，superkernel W¯¯的\（\ mathcal r \）是合理的功能自双超空间，人口是在一个标准双射在各种各向同性全superflags的W¯¯与设定的对称完全分解\(\mathcal R\)。特别地，我们的结果适用于类型d的甚至李代数的情况下\（{} _米\）对应于\（\ mathfrak {OSP} _ {2米| 0} = \ mathfrak {所以} _ {2米} \） .