Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of 𝔤𝔩_{𝔑}

Mukhin, E.; Tarasov, V.; Varchenko, A.

doi:10.1090/S1061-0022-2011-01152-5

Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of $\mathfrak {gl}_N$
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by E. Mukhin, V. Tarasov and A. Varchenko

St. Petersburg Math. J. 22 (2011), 463-472

DOI: https://doi.org/10.1090/S1061-0022-2011-01152-5

Published electronically: March 18, 2011

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Abstract:

It is shown that the Gaudin Hamiltonians $H_1$, …, $H_n$ generate the Bethe algebra of the $n$-fold tensor power of the vector representation of $\mathfrak {gl}_N$. 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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