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

Understand

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.