Bethe eigenvectors of higher transfer matrices

Details Bethe eigenvectors of higher transfer matrices Bethe eigenvectors of higher transfer matrices

2006-04-30

arxiv.org/abs/math/0605015v2

J. Stat. Mech. Theory Exp. 2006, no.8, P08002, 1-44. (electronic)

Mathematics

Quantum Algebra

48 pages, amstex.tex (ver 2.2), misprints corrected

Scientific paper

10.1088/1742-5468/2006/08/P08002

We consider the XXX-type and Gaudin quantum integrable models associated with the Lie algebra $gl_N$. The models are defined on a tensor product irreducible $gl_N$-modules. For each model, there exist $N$ one-parameter families of commuting operators on the tensor product, called the transfer matrices. We show that the Bethe vectors for these models, given by the algebraic nested Bethe ansatz are eigenvectors of higher transfer matrices and compute the corresponding eigenvalues.

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