The argument shift method and the Gaudin model
The argument shift method and the Gaudin model
复制标题
参数平移法和高丁模型
DOI：
10.1007/s10688-006-0030-3
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发表时间：
2006
影响因子：
0.4
通讯作者：
L. Rybnikov
中科院分区：
文献类型：
--
作者：
L. Rybnikov
We construct a family of maximal commutative subalgebras in the tensor product ofncopies of the universal enveloping algebraU() of a semisimple Lie algebra. This family is parameterized by finite sequences µ,z1, ...,zn, where µ ∈*andzi∈ ℂ. The construction presented here generalizes the famous construction of the higher Gaudin Hamiltonians due to Feigin, Frenkel, and Reshetikhin. Forn= 1, the corresponding commutative subalgebras in the Poisson algebraS() were obtained by Mishchenko and Fomenko with the help of the argument shift method. For commutative algebras of our family, we establish a connection between their representations in the tensor products of finite-dimensional-modules and the Gaudin model.
