On separation of variables and completeness of the Bethe ansatz for quantum gl_N Gaudin model

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dc.creatorMukhin, E.
dc.creatorTarasov, V.
dc.creatorVarchenko, A.
dc.date2007-12-06
dc.date.accessioned2026-07-07T08:47:42Z
dc.date.available2026-07-07T08:47:42Z
dc.descriptionIn this note, we discuss implications of the results obtained in [MTV4]. It was shown there that eigenvectors of the Bethe algebra of the quantum gl_N Gaudin model are in a one-to-one correspondence with Fuchsian differential operators with polynomial kernel. Here, we interpret this fact as a separation of variables in the gl_N Gaudin model. Having a Fuchsian differential operator with polynomial kernel, we construct the corresponding eigenvector of the Bethe algebra. It was shown in [MTV4] that the Bethe algebra has simple spectrum if the evaluation parameters of the Gaudin model are generic. In that case, our Bethe ansatz construction produces an eigenbasis of the Bethe algebra.
dc.descriptionLatex, 9 pages
dc.identifierhttps://arxiv.org/abs/0712.0981
dc.identifierhttp://arxiv.org/abs/0712.0981
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143692
dc.subjectQuantum Algebra
dc.subjectAlgebraic Geometry
dc.titleOn separation of variables and completeness of the Bethe ansatz for quantum gl_N Gaudin model
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