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

2009/04/14 by Mukhin, E., Tarasov, V., Varchenko, A.
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0904.2131

Abstract

We show that the Gaudin Hamiltonians H₁,...,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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