Abstract We establish a duality of the non-periodic Gaudin model associated with superalgebra gl m | n and the non-periodic Gaudin model associated with algebra gl k . The Hamiltonians of the Gaudin models are given by expansions of a Berezinian of an ( m + n ) × ( m + n ) matrix in the case of gl m | n and of a column determinant of a k × k matrix in the case of gl k . We obtain our results by proving Capelli type identities for both cases and comparing the results.

中文翻译：

---

glm|n 和 glk Gaudin 模型的对偶性

摘要 我们建立了与超代数 gl m | 相关的非周期 Gaudin 模型的对偶性。n 和与代数 gl k 相关的非周期 Gaudin 模型。在 gl m | 的情况下，Gaudin 模型的哈密顿量由 ( m + n ) × ( m + n ) 矩阵的 Berezinian 的展开给出。在 gl k 的情况下，n 和 ak × k 矩阵的列行列式。我们通过证明两种情况的 Capelli 类型身份并比较结果来获得我们的结果。