Gaudin Hamiltonians generate the Bethe algebra of a tensor power of vector representation of gl_N
E. Mukhin, V. Tarasov, A. Varchenko
TL;DR
This paper demonstrates that Gaudin Hamiltonians generate the Bethe algebra for tensor powers of gl_N's vector representation, revealing a N-independent formula that aligns with Wilson's stationary Baker-Akhiezer function.
Contribution
It establishes a N-independent formula linking Gaudin Hamiltonians to the Bethe algebra, connecting representation theory with algebraic geometry.
Findings
Gaudin Hamiltonians generate the Bethe algebra for tensor powers of gl_N.
The generator formula is independent of N.
The formula matches Wilson's stationary Baker-Akhiezer function.
Abstract
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons