On separation of variables and completeness of the Bethe ansatz for quantum gl N Gaudin model - Mathematics > Quantum AlgebraReportar como inadecuado




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Abstract: In this note, we discuss implications of the results obtained in MTV4. Itwas shown there that eigenvectors of the Bethe algebra of the quantum gl NGaudin model are in a one-to-one correspondence with Fuchsian differentialoperators with polynomial kernel. Here, we interpret this fact as a separationof variables in the gl N Gaudin model. Having a Fuchsian differential operatorwith polynomial kernel, we construct the corresponding eigenvector of the Bethealgebra. It was shown in MTV4 that the Bethe algebra has simple spectrum ifthe evaluation parameters of the Gaudin model are generic. In that case, ourBethe ansatz construction produces an eigenbasis of the Bethe algebra.



Autor: E. Mukhin, V. Tarasov, A. Varchenko

Fuente: https://arxiv.org/







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