论文标题
$ \ mathbb {c} [\ mathfrak {s} _n] $ bethe subalgebra中的身份
An identity in the Bethe subalgebra of $\mathbb{C}[\mathfrak{S}_n]$
论文作者
论文摘要
作为Bethe Ansatz猜想的一部分，Gaudin模型的$ \ Mathfrak {gl} _n $，Mukhin，Tarasov和Varchenko描述了多条件的逆沃尔森克人与高丹汉密尔顿人的特征性的wronskians之间的对应关系。值得注意的是，这种信件为Shapiro-Shapiro猜想提供了第一个证明。在本文中，我们在对称组的组代数中给出了一个身份，该代数允许人们直接建立对应关系，而无需使用Bethe Ansatz。
As part of the proof of the Bethe ansatz conjecture for the Gaudin model for $\mathfrak{gl}_n$, Mukhin, Tarasov, and Varchenko described a correspondence between inverse Wronskians of polynomials and eigenspaces of the Gaudin Hamiltonians. Notably, this correspondence afforded the first proof of the Shapiro-Shapiro conjecture. In the present paper, we give an identity in the group algebra of the symmetric group, which allows one to establish the correspondence directly, without using the Bethe ansatz.
