论文标题
与GL相关的Gaudin模型的Bethe Ansatz的完整性（1 | 1）
Completeness of Bethe ansatz for Gaudin models associated with gl(1|1)
论文作者
论文摘要
我们研究了与$ \ Mathfrak {gl}（1 | 1）$相关的Gaudin模型。我们对汉密尔顿（高丁·哈密顿人）代数的明确描述作用于多项式评估的张量产物$ \ mathfrak {gl}（1 | 1）[t] $ - 模块。因此，以最高权重和评估参数为例，汉密尔顿代数的常见特征向量（达到比例性）与明确多项式的一元分隔线之间存在两次培养。特别是，我们的结果意味着，汉密尔顿代数的每个共同特征空间都有一个维度。因此，我们从Arxiv确认了猜想8.3：1809.01279。我们还给出了广义特征空间的尺寸。此外，我们以二次Gaudin传输矩阵和$ \ Mathrm {U}（\ Mathfrak {\ Mathfrak {gl}（gl}（gl}（1 | 1 | 1）[t] [t]）$，我们表达了与反隔离剂相关的高丁转移矩阵的生成伪分差操作员。
We study the Gaudin models associated with $\mathfrak{gl}(1|1)$. We give an explicit description of the algebra of Hamiltonians (Gaudin Hamiltonians) acting on tensor products of polynomial evaluation $\mathfrak{gl}(1|1)[t]$-modules. It follows that there exists a bijection between common eigenvectors (up to proportionality) of the algebra of Hamiltonians and monic divisors of an explicit polynomial written in terms of the highest weights and evaluation parameters. In particular, our result implies that each common eigenspace of the algebra of Hamiltonians has dimension one. Therefore, we confirm Conjecture 8.3 from arXiv:1809.01279. We also give dimensions of the generalized eigenspaces. Moreover, we express the generating pseudo-differential operator of Gaudin transfer matrices associated to antisymmetrizers in terms of the quadratic Gaudin transfer matrix and the center of $\mathrm{U}(\mathfrak{gl}(1|1)[t])$.
