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Article

Limits of Gaudin algebras, quantization of bending flows, Jucys-Murphy elements and Gelfand-Tsetlin bases

Letters in Mathematical Physics. 2010. Vol. 91. No. 1. P. 129-150.
Rybnikov L. G., Chervov A., Falqui G.
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 z1; : : : ; zn . We obtain some new commutative subalgebras in U(g)­n as limit cases of Gaudin subalgebras. These commutative subalgebras turn to be related to the Hamiltonians of bending °ows and to the Gelfand{Tsetlin bases. We use this to prove the simplicity of spectrum in the Gaudin model for some new cases.