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- W2084967443 abstract "We construct a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra U ( $$mathfrak{g}$$ ) of a semisimple Lie algebra $$mathfrak{g}$$ . This family is parameterized by finite sequences µ, z 1, ..., z n , where µ ∈ $$mathfrak{g}$$ * and z i ∈ ℂ. The construction presented here generalizes the famous construction of the higher Gaudin Hamiltonians due to Feigin, Frenkel, and Reshetikhin. For n = 1, the corresponding commutative subalgebras in the Poisson algebra S( $$mathfrak{g}$$ ) 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 $$mathfrak{g}$$ -modules and the Gaudin model." @default.
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- W2084967443 date "2006-07-01" @default.
- W2084967443 modified "2023-10-09" @default.
- W2084967443 title "The argument shift method and the Gaudin model" @default.
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- W2084967443 doi "https://doi.org/10.1007/s10688-006-0030-3" @default.
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