Gaudin Hamiltonians generate the Bethe algebra of a tensor power of vector representation of gl_N

Details Gaudin Hamiltonians generate the Bethe algebra of a tensor power of vector representation of gl_N Gaudin Hamiltonians generate the Bethe algebra of a tensor power of vector representation of gl_N

2009-04-14

arxiv.org/abs/0904.2131v1

Mathematics

Quantum Algebra

Latex, 11 pages

Scientific paper

We show that the Gaudin Hamiltonians H_1,...,H_n generate the Bethe algebra of the n-fold tensor power of the vector representation of gl_N. Surprisingly the formula for the generators of the Bethe algebra in terms of the Gaudin Hamiltonians does not depend on N. Moreover, this formula coincides with Wilson's formula for the stationary Baker-Akhiezer function on the adelic Grassmannian.

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