Gaudin代数的极限，弯曲流的量子化，Jucys-Murphy元和Gelfand-Tsetlin基
Limits of Gaudin algebras, quantization of bending flows, Jucys--Murphy elements and Gelfand--Tsetlin bases
摘要：
Gaudin代数在半单李代数$\g$的泛包络代数$U(\g)$的$n$副本的张量积中形成一族极大交换子代数。该族由成对不同复数$z_1,...,z_n$的集合参数化。我们得到了$U(\g)^{\otimes n}$中的一些新的交换子代数作为Gaudin子代数的极限情形.这些交换子代数转而与弯曲流的哈密顿量和Gelfand-Tsetlin基有关。我们利用这一点证明了Gaudin模型在一些新情况下谱的简单性。
英文摘要：
Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of $n$ copies of the universal enveloping algebra $U(\g)$ of a semisimple Lie algebra $\g$. This family is parameterized by collections of pairwise distinct complex numbers $z_1,...,z_n$. We obtain some new commutative subalgebras in $U(\g)^{\otimes n}$ as limit cases of Gaudin subalgebras. These commutative subalgebras turn to be related to the hamiltonians of bending flows and to the Gelfand--Tsetlin bases. We use this to prove the simplicity of spectrum in the Gaudin model for some new cases.
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